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PSLE

PSLE Foundation Mathematics

<p>$x = -3$ and $y = 4$ is a pair of solutions to the following simultaneous equations:</p>
<p style="text-align: center">$x + 3y = p$</p>
<p style="text-align: center">$ \qquad\quad qx - 5 = y^2 - \frac{2}{3}py$</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the values of $p$ and $q$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence find the other pair of solutions to the simultaneous equations.</span></div></li></ol>

$x = -3$ and $y = 4$ is a pair of solutions to the following simultaneous equations:

$ \qquad\quad qx - 5 = y^2 - \frac{2}{3}py$

Hence find the other pair of solutions to the simultaneous equations.

Linear and Non-Linear Simultaneous Equations

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q16

Simultaneous Equations

<p>In the diagram, $ABCD$ consists of $6$ identical rectangles. Given that each one of the $6$ rectangles has an area of $112\text{ cm}^2$ with $AB &lt; BP$ and the perimeter of $ABCD$ is $184\text{ cm}$, find the perimeter of $ABPQ$.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1770448366220-iuybmj8ektj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzA0NDgzNjYyMjAtaXV5Ym1qOGVrdGoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUwNzYyNywiZXhwIjoxNzkzNTA3OTI3fQ.BmZOb6-ZkYSFEnAcuqLJd_reRkiNwYeBYSntBdeJBfk" style="max-width: min(300px, 100%); height: auto; display: block;" alt="Diagram showing rectangle ABCD divided into 6 identical smaller rectangles" class="aligncenter custom-width" /></figure></div>

In the diagram, $ABCD$ consists of $6$ identical rectangles. Given that each one of the $6$ rectangles has an area of $112\text{ cm}^2$ with $AB < BP$ and the perimeter of $ABCD$ is $184\text{ cm}$, find the perimeter of $ABPQ$.

Perimeter and Area of Rectangles and Squares

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q15

Perimeter and Area of Plane Figures

<p>Solve the simultaneous equations</p>
<p style="text-align: center">$ \,\,\, 3x^{2} + xy = 2y^{2} - 5$</p>
<p style="text-align: center">$x^{2} + 2xy = 1 - y^{2}$</p>

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q14

<p>Solve the simultaneous equations</p>
<p style="text-align: center">$ \quad\,\,\, xy = 2^{11}$</p>
<p style="text-align: center">$\frac{x}{y} - \frac{y}{x} = \frac{63}{8}$</p>

$\frac{x}{y} - \frac{y}{x} = \frac{63}{8}$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q13

<p>Solve the simultaneous equations</p>
<p style="text-align: center">$ \qquad\, x - y = 5$<br>$\frac{y}{y+7} - \frac{3x+8}{4-x^2} = \frac{5}{y+3}$</p>

$ \qquad\, x - y = 5$
$\frac{y}{y+7} - \frac{3x+8}{4-x^2} = \frac{5}{y+3}$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q7

<p>Solve the simultaneous equations</p>
<p style="text-align: center">$ \qquad\quad\;\,\, 15y - 8x = 39$<br>$(x + 3)^2 + (y - 1)^2 = 17^2$</p>

$ \qquad\quad\;\,\, 15y - 8x = 39$
$(x + 3)^2 + (y - 1)^2 = 17^2$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q6

<p>Solve the simultaneous equations</p>
<p style="text-align: center">$2x^2 + 5xy + 3y^2 = 4$<br>$ \qquad\qquad xy + 2 = 0$</p>

$2x^2 + 5xy + 3y^2 = 4$
$ \qquad\qquad xy + 2 = 0$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q5

<p>Solve the simultaneous equations</p>
<p style="text-align: center">$ \quad\quad\: 2x = 5y - 3$<br>$4x^2 - 2y^2 = 6xy - 1$</p>

$ \quad\quad\: 2x = 5y - 3$
$4x^2 - 2y^2 = 6xy - 1$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q4

<p>Solve the simultaneous equations</p>
<p style="text-align: center">$ \qquad\qquad\: x - y = -1$<br>$x^2 + 2(y + 1)^2 = 3$</p>

$ \qquad\qquad\: x - y = -1$
$x^2 + 2(y + 1)^2 = 3$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q3

<p>Solve the simultaneous equations</p>
<p style="text-align: center">$x + 3 = y$<br>$x + \frac{2}{y} = 0$</p>

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q2

<p>Solve the simultaneous equations</p>
<p style="text-align: center">$ \;\:\: 2x + 5y = 2$<br>$4x^2 - 17y^2 = 16$</p>

$ \;\:\: 2x + 5y = 2$
$4x^2 - 17y^2 = 16$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q1

<p>The graph of $y={{x}^{3}}-4{{x}^{2}}+8x+c$ is shown.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li><div class="list-item-paragraph">State the value of $c$.</div></li><li><div class="list-item-paragraph">Explain if&nbsp;${{x}^{3}}-4{{x}^{2}}+8x+c$ can be expressed as a product of three linear factors.</div></li><li><div class="list-item-paragraph">Find the linear factor of ${{x}^{3}}-4{{x}^{2}}+8x+c$ and hence find the value of $x$-intercept of the curve. </div></li><li><div class="list-item-paragraph">Find the coordinates of the intersection points of the curve $y={{x}^{3}}-4{{x}^{2}}+8x+c$ and the line $y=7x-21$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1766070081795-14sk0uy8wqj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjYwNzAwODE3OTUtMTRzazB1eTh3cWoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUwNzYyNywiZXhwIjoxNzkzNTA3OTI3fQ.1ERtWz6DgbgTgK5UjJZBPLa7rt96UoHHUtX1TZJ9PX8" style="max-width: min(130px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The graph of $y={{x}^{3}}-4{{x}^{2}}+8x+c$ is shown.

Cubic Expressions and Equations

Remainder and Factor Theorems

Polynomial Functions and Key Features

Polynomials, Cubic Equations and Partial Fractions

<p>A positive whole number has two digits which can be expressed as $10x+y$ where $x&gt;y$. When the two digits are reversed, a new number is formed.  The difference between the squares of the two numbers is $1584$.  The sum of the two numbers is $44$ times the difference between the digits of the original number.  Find the two numbers.</p>

A positive whole number has two digits which can be expressed as $10x+y$ where $x>y$. When the two digits are reversed, a new number is formed.  The difference between the squares of the two numbers is $1584$.  The sum of the two numbers is $44$ times the difference between the digits of the original number.  Find the two numbers.

<p>Solve the simultaneous equations.</p>
<p style="text-align: center">\begin{matrix}
  & 2x-5y+17=0 \\ 
 & \qquad\qquad\;\, xy=6  
\end{matrix}
</p>

\begin{matrix}
  & 2x-5y+17=0 \\ 
 & \qquad\qquad\;\, xy=6  
\end{matrix}


<p>Find the coordinates of the points of intersection of the graphs with equations $3=x-2y$ and $xy=20-3y$.</p>

Find the coordinates of the points of intersection of the graphs with equations $3=x-2y$ and $xy=20-3y$.

<p>Find the coordinates of the points of intersection of the line $2x + y = 3$ and the curve $3x^2 - y^2 + 4xy - 6 = 0$.</p>

Find the coordinates of the points of intersection of the line $2x + y = 3$ and the curve $3x^2 - y^2 + 4xy - 6 = 0$.

<p>A garden is of the shape $ABCDE$ as shown in the diagram below. $AB$ and $DC$are perpendicular to $BC$.  It is given that&nbsp;$AE=DE=5x$m , $AB=DC=y$m and $BC=6x$m.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li data-list-item-id="item-1788064028056-zmp8mjy16" data-list-item-path="item-1788064028056-zmp8mjy16"><div class="list-item-paragraph"><p>Find an expression, in terms of $x$, for the length of $EK$.</p></div></li><li data-list-item-id="item-1788064028761-1tf70nm6s" data-list-item-path="item-1788064028761-1tf70nm6s"><div class="list-item-paragraph"><p>The perimeter and area of the garden are $54$ m and $180$ m$^{2}$ respectively. Write down a pair of simultaneous equations relating $x$ and $y$.</p></div></li><li data-list-item-id="item-1788064029564-rekkt3adc" data-list-item-path="item-1788064029564-rekkt3adc"><div class="list-item-paragraph"><p>Solve the pair of simultaneous equations to find the values of $x$ and $y$.</p></div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="graph-block" data-graph-config="eyJib3VuZGluZ0JveCI6Wy00LjcyMDAwMDAwMDAwMDAwMSw0LjM1LDQuNDIsLTUuNjJdLCJ3aWR0aCI6MzAwLCJoZWlnaHQiOjMwMCwiYXhpcyI6ZmFsc2UsImdyaWQiOmZhbHNlLCJncmlkU2V0dGluZ3MiOnsibWFqb3JTdGVwWCI6MSwibWFqb3JTdGVwWSI6MSwibWlub3JFbGVtZW50c1giOjQsIm1pbm9yRWxlbWVudHNZIjo0LCJzaG93TWFqb3JHcmlkTGluZXMiOnRydWUsInNob3dNaW5vckdyaWRMaW5lcyI6dHJ1ZSwibWFqb3JDb2xvciI6IiM5NGEzYjgiLCJtYWpvck9wYWNpdHkiOjAuNDUsIm1ham9yU3Ryb2tlV2lkdGgiOjAuOCwibWlub3JDb2xvciI6IiNjYmQ1ZTEiLCJtaW5vck9wYWNpdHkiOjAuNDUsIm1pbm9yU3Ryb2tlV2lkdGgiOjAuNX0sImtlZXBBc3BlY3RSYXRpbyI6dHJ1ZSwic2hvd05hdmlnYXRpb24iOmZhbHNlLCJzaG93QXhpc0xhYmVscyI6ZmFsc2UsInhUaWNrTGFiZWxFdmVyeSI6MSwieVRpY2tMYWJlbEV2ZXJ5IjoxLCJ4QXhpc0xhYmVsIjoiXFwoeFxcKSIsInlBeGlzTGFiZWwiOiJcXCh5XFwpIiwib3JpZ2luTGFiZWwiOiJcXChPXFwpIiwieEF4aXNMYWJlbE9mZnNldCI6WzIsLTExXSwieUF4aXNMYWJlbE9mZnNldCI6Wy0xNCw1XSwib3JpZ2luTGFiZWxPZmZzZXQiOlstNSwtMl0sImVsZW1lbnRzIjpbeyJpZCI6IjZiMDJlMzhlLWYwODItNGMyMC1iM2EwLTIyMDI2ZmU5Mjg0YyIsInR5cGUiOiJzZWdtZW50IiwiZml4ZWQiOnRydWUsInBvaW50MSI6Wy0zLDBdLCJwb2ludDIiOlswLDNdLCJjb2xvciI6IiMwMDAwMDAiLCJzdHJva2VXaWR0aCI6MS41fSx7ImlkIjoiMmRmMGFiODEtYmNlYi00YWYxLTlhODktMDVmZmU1NTg4MDBkIiwidHlwZSI6InNlZ21lbnQiLCJmaXhlZCI6dHJ1ZSwicG9pbnQxIjpbMCwzXSwicG9pbnQyIjpbMywwXSwiY29sb3IiOiIjMDAwMDAwIiwic3Ryb2tlV2lkdGgiOjEuNX0seyJpZCI6IjNlMTU5YzUzLWQxZTUtNGM3ZS1hMGJlLWEwYWVlOTczNTg2YyIsInR5cGUiOiJzZWdtZW50IiwiZml4ZWQiOnRydWUsInBvaW50MSI6Wy0zLDBdLCJwb2ludDIiOlstMywtNF0sImNvbG9yIjoiIzAwMDAwMCIsInN0cm9rZVdpZHRoIjoxLjV9LHsiaWQiOiI3OTUzMjcyYi04YzMxLTQ3ODAtOTk2My1jZWY3ZjkwZWUzNzciLCJ0eXBlIjoic2VnbWVudCIsImZpeGVkIjp0cnVlLCJwb2ludDEiOlstMywtNF0sInBvaW50MiI6WzMsLTRdLCJjb2xvciI6IiMwMDAwMDAiLCJzdHJva2VXaWR0aCI6MS41fSx7ImlkIjoiOTEzNGVhNTUtZjE5Ni00ZmQ2LWI4ZjYtNzIwOGRkMDVhNmY5IiwidHlwZSI6InNlZ21lbnQiLCJmaXhlZCI6dHJ1ZSwicG9pbnQxIjpbMywtNF0sInBvaW50MiI6WzMsMF0sImNvbG9yIjoiIzAwMDAwMCIsInN0cm9rZVdpZHRoIjoxLjV9LHsiaWQiOiI1MzU5MTQ2Mi1mM2QzLTQ4ZWItYjE4NS1mYWI2NmFhNmU0NjgiLCJ0eXBlIjoic2VnbWVudCIsImZpeGVkIjp0cnVlLCJwb2ludDEiOlstMywwXSwicG9pbnQyIjpbMywwXSwiY29sb3IiOiIjMDAwMDAwIiwic3Ryb2tlV2lkdGgiOjEuNSwiZGFzaCI6Mn0seyJpZCI6ImU5ZGMyNGFiLTgxMWMtNDkyOS1iZjQyLTk3NmM4NDUwZjAzYiIsInR5cGUiOiJzZWdtZW50IiwiZml4ZWQiOnRydWUsInBvaW50MSI6WzAsM10sInBvaW50MiI6WzAsMF0sImNvbG9yIjoiIzAwMDAwMCIsInN0cm9rZVdpZHRoIjoxLjUsImRhc2giOjJ9LHsiaWQiOiJjNjE4ODgyNC03N2U4LTRmZTUtYmQ2Zi1mZmVmNjRmNDlhOWIiLCJ0eXBlIjoicG9seWxpbmUiLCJmaXhlZCI6dHJ1ZSwicG9pbnRzIjpbWy0zLC0zLjYyXSxbLTIuNjIsLTMuNjJdLFstMi42MiwtNF1dLCJjb2xvciI6IiMwMDAwMDAiLCJzdHJva2VXaWR0aCI6MS41fSx7ImlkIjoiMTFkM2RiYjMtNzdiOS00ZTA4LWI0ZjYtY2Y2YzA0NDFmNjkwIiwidHlwZSI6InBvbHlsaW5lIiwiZml4ZWQiOnRydWUsInBvaW50cyI6W1szLC0zLjYyXSxbMi42MiwtMy42Ml0sWzIuNjIsLTRdXSwiY29sb3IiOiIjMDAwMDAwIiwic3Ryb2tlV2lkdGgiOjEuNX0seyJpZCI6IjYzYmFhZDc4LTEzODEtNDRhMS04YTc4LTA4ZDcwZTcwYTExNSIsInR5cGUiOiJwb2x5bGluZSIsImZpeGVkIjp0cnVlLCJwb2ludHMiOltbMCwwXSxbMCwwLjM4XSxbMC4zOCwwLjM4XSxbMC4zOCwwXSxbMCwwXV0sImNvbG9yIjoiIzAwMDAwMCIsInN0cm9rZVdpZHRoIjoxLjV9LHsiaWQiOiIyYzg2ZGJhYy00NjAxLTRiYjktYTUwOS01YmVlMDIxYmQ2NzMiLCJ0eXBlIjoidGV4dCIsImZpeGVkIjp0cnVlLCJ4IjotMy41MiwieSI6MC4wMiwibGFiZWwiOiJcXChBXFwpIiwiY29sb3IiOiIjMDAwMDAwIiwic3Ryb2tlV2lkdGgiOjEuNX0seyJpZCI6ImQzZWY4NWFjLWNlMWItNDI1Zi1iMWY0LThjMGIxZGU1MTk2YSIsInR5cGUiOiJ0ZXh0IiwiZml4ZWQiOnRydWUsIngiOi0zLjUyLCJ5IjotNC4zNSwibGFiZWwiOiJcXChCXFwpIiwiY29sb3IiOiIjMDAwMDAwIiwic3Ryb2tlV2lkdGgiOjEuNX0seyJpZCI6ImUwZmEyMmEyLWJhMjctNGM3Mi04OGYwLTE3MmVkNWYxOTU4YSIsInR5cGUiOiJ0ZXh0IiwiZml4ZWQiOnRydWUsIngiOjMuMTgsInkiOi00LjM1LCJsYWJlbCI6IlxcKENcXCkiLCJjb2xvciI6IiMwMDAwMDAiLCJzdHJva2VXaWR0aCI6MS41fSx7ImlkIjoiZjRjMTVkY2MtMTQzYi00MGM4LTg1NTAtZGIxZTFhMWNhMmFiIiwidHlwZSI6InRleHQiLCJmaXhlZCI6dHJ1ZSwieCI6My4xOCwieSI6MC4wMiwibGFiZWwiOiJcXChEXFwpIiwiY29sb3IiOiIjMDAwMDAwIiwic3Ryb2tlV2lkdGgiOjEuNX0seyJpZCI6IjBjNzAyNDY3LTI0YWYtNDY0Ny1iZDE5LWY5YmYzZWMzYmJkMSIsInR5cGUiOiJ0ZXh0IiwiZml4ZWQiOnRydWUsIngiOi0wLjE1LCJ5IjozLjM1LCJsYWJlbCI6IlxcKEVcXCkiLCJjb2xvciI6IiMwMDAwMDAiLCJzdHJva2VXaWR0aCI6MS41fSx7ImlkIjoiODY2MjFiN2ItN2Q0NC00OTZhLTg3YmYtODI3ZDEzMTM0ODA0IiwidHlwZSI6InRleHQiLCJmaXhlZCI6dHJ1ZSwieCI6LTAuMTgsInkiOi0wLjQyLCJsYWJlbCI6IlxcKEtcXCkiLCJjb2xvciI6IiMwMDAwMDAiLCJzdHJva2VXaWR0aCI6MS41fSx7ImlkIjoiNGNiYTYyMTItZmY3Mi00YTA4LWFmMGMtYjhlZjA5Mjk1ODkzIiwidHlwZSI6InRleHQiLCJmaXhlZCI6dHJ1ZSwieCI6LTIuMTgsInkiOjEuNzIsImxhYmVsIjoiXFwoNXhcXCkiLCJjb2xvciI6IiMwMDAwMDAiLCJzdHJva2VXaWR0aCI6MS41fSx7ImlkIjoiY2U5MGM1NTYtYzMwMC00NGY3LWE5OWEtZGQwMmJiMTVkMDVhIiwidHlwZSI6InRleHQiLCJmaXhlZCI6dHJ1ZSwieCI6MS42NSwieSI6MS43MiwibGFiZWwiOiJcXCg1eFxcKSIsImNvbG9yIjoiIzAwMDAwMCIsInN0cm9rZVdpZHRoIjoxLjV9LHsiaWQiOiJjYTQ1YjAyNC0xZTI5LTQ1YzgtYTc2MC00N2YzMjI5N2MwODEiLCJ0eXBlIjoidGV4dCIsImZpeGVkIjp0cnVlLCJ4IjotMy43MiwieSI6LTIuMSwibGFiZWwiOiJcXCh5XFwpIiwiY29sb3IiOiIjMDAwMDAwIiwic3Ryb2tlV2lkdGgiOjEuNX0seyJpZCI6IjcwNmQwYmMyLWIwNGMtNGE3Ni1iZDFkLWMzNzY2MTJjOTU2MiIsInR5cGUiOiJ0ZXh0IiwiZml4ZWQiOnRydWUsIngiOjMuNDIsInkiOi0yLjEsImxhYmVsIjoiXFwoeVxcKSIsImNvbG9yIjoiIzAwMDAwMCIsInN0cm9rZVdpZHRoIjoxLjV9LHsiaWQiOiI1ZjY3NGZiNi1kMWNiLTQyNDYtOGM1Mi02ZGJkYjU4MGMzM2MiLCJ0eXBlIjoidGV4dCIsImZpeGVkIjp0cnVlLCJ4IjotMC4zLCJ5IjotNC42MiwibGFiZWwiOiJcXCg2eFxcKSIsImNvbG9yIjoiIzAwMDAwMCIsInN0cm9rZVdpZHRoIjoxLjV9XSwic2hvd1hBeGlzIjpmYWxzZSwic2hvd1lBeGlzIjpmYWxzZX0=" data-width="300" data-height="300" style="width:300px;height:300px;max-width:100%;display:block;margin:0 auto;"></div></div></div></div>

A garden is of the shape $ABCDE$ as shown in the diagram below. $AB$ and $DC$are perpendicular to $BC$.  It is given that $AE=DE=5x$m , $AB=DC=y$m and $BC=6x$m.

<p>A solid rectangular block has a square base of side $x$ cm and height of $y$ cm.  The total surface area of the rectangular block is $90$ cm$^{2}$ and the total length of the $12$ edges is $48$ cm.  Show that&nbsp;${{x}^{2}}-8x+15=0$ and find the possible values of $x$ and of $y$.</p>

A solid rectangular block has a square base of side $x$ cm and height of $y$ cm.  The total surface area of the rectangular block is $90$ cm$^{2}$ and the total length of the $12$ edges is $48$ cm.  Show that ${{x}^{2}}-8x+15=0$ and find the possible values of $x$ and of $y$.

<p>Solve the simultaneous equations, </p>
<p style="text-align: center">$xy-3x-11=0$</p>
<p style="text-align: center">$3y=x+1$</p>
<p>Hence, state the coordinates of the points of intersections between the curve, $xy-3x-11=0$ and the line, $3y=x+1$.</p>

Hence, state the coordinates of the points of intersections between the curve, $xy-3x-11=0$ and the line, $3y=x+1$.

<p>Solve the following simultaneous equations.</p>
<ol class="i-list"><li><div class="list-item-paragraph">$\frac{5x}{{{y}^{2}}}+x=21$</div><div class="list-item-paragraph">$\frac{3x}{{{y}^{2}}}-4x=-3.5$</div></li><li><div class="list-item-paragraph">${{\left( \frac{1}{x}+\frac{1}{y} \right)}^{2}}=157+\frac{2}{xy}$</div><div class="list-item-paragraph">${{\left( \frac{1}{x} \right)}^{2}}-{{\left( \frac{1}{y} \right)}^{2}}=85$</div></li><li><div class="list-item-paragraph">$\frac{5}{x+y}+\frac{1}{x-y}=9$</div><div class="list-item-paragraph">$\frac{2}{x+y}-\frac{3}{x-y}=7$</div></li><li><div class="list-item-paragraph">$\frac{4}{\sqrt[3]{x}}-\frac{3}{\sqrt[3]{y}}=9\frac{1}{2}$</div><div class="list-item-paragraph">$\frac{1}{6\left( \sqrt[3]{x} \right)}-\frac{2}{3\left( \sqrt[3]{y} \right)}=\frac{2}{3}$</div></li></ol>

Solve the following simultaneous equations.

Math Question Bank