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Solve the simultaneous equations.
$x-2y=8$ $3^x(27^y)=9$

Simultaneous Equations

Solve the simultaneous equations
$x + 3y + 2z = \frac{5}{2}$
$ \;\;\, 2x + 4y + z = - \, \frac{1}{2}$
$ \;\;\, \frac{1}{2}x + y - 3z = -5$

$ \;\;\, 2x + 4y + z = - \, \frac{1}{2}$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q18

Solve the simultaneous equations
${5x + 3y = 12}$
${ \,\,\, z - y = 7}$
${ \qquad\quad\,\, 3x = z + 5}$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q17

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

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

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 $ABPQ$.
<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=eyJraWQiOiJzdG9yYWdlLXVybC1zaWduaW5nLWtleV9iZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzA0NDgzNjYyMjAtaXV5Ym1qOGVrdGoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4NTc4MDE2MCwiZXhwIjoxNzg1NzgwNDYwfQ.1SiGjzMVKZmkThReXkkQfnFRMpO5Nom-lFmjhHrzZBc" 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 $ABPQ$.

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

Solve the simultaneous equations
$ \,\,\, 3x^{2} + xy = 2y^{2} - 5$
$x^{2} + 2xy = 1 - y^{2}$

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

Solve the simultaneous equations
$ \quad\,\,\, xy = 2^{11}$
$\frac{x}{y} - \frac{y}{x} = \frac{63}{8}$

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

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

Solve the simultaneous equations
$ \,\, \frac{4}{\sqrt[3]{x}}-\frac{3}{\sqrt[3]{y}}=\frac{19}{2}$
$\frac{1}{\sqrt[3]{x}}-\frac{4}{\sqrt[3]{y}}=4$

$ \,\, \frac{4}{\sqrt[3]{x}}-\frac{3}{\sqrt[3]{y}}=\frac{19}{2}$

$\frac{1}{\sqrt[3]{x}}-\frac{4}{\sqrt[3]{y}}=4$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q12

Solve the simultaneous equations
$\frac{5}{x+y} + \frac{1}{x-y} = 9$
$\frac{2}{x+y} - \frac{3}{x-y} = 7$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q11

Solve the simultaneous equations
$ \qquad\qquad\, \left(\frac{1}{x}+\frac{1}{y}\right)^2 = \frac{2}{xy} + 157 $
$ \left(\frac{1}{x}\right)^2 - \left(\frac{1}{y}\right)^2 = 85 $

$ \qquad\qquad\, \left(\frac{1}{x}+\frac{1}{y}\right)^2 = \frac{2}{xy} + 157 $

$ \left(\frac{1}{x}\right)^2 - \left(\frac{1}{y}\right)^2 = 85 $

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q10

Solve the simultaneous equations
$ \, \frac{5x}{y^2} + x = 21$ $\frac{3x}{y^2} - 4x = - \ \frac{7}{2}$

$ \, \frac{5x}{y^2} + x = 21$
$\frac{3x}{y^2} - 4x = - \ \frac{7}{2}$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q9

Solve the simultaneous equations
$ \qquad\;\;\;\, x^2 + y^2 = 7$ $(x - y)(x + y) = 1$

$ \qquad\;\;\;\, x^2 + y^2 = 7$
$(x - y)(x + y) = 1$

IP2U4 and 3EMU1 SW - Non-Linear Simultaneous Equations Worksheet Q8

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

$ \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

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

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

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

Solve the simultaneous equations
$2x^2 + 5xy + 3y^2 = 4$ $ \qquad\qquad xy + 2 = 0$

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

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

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

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

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

Solve the simultaneous equations
$ \qquad\qquad\: x - y = -1$ $x^2 + 2(y + 1)^2 = 3$

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

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

Solve the simultaneous equations
$x + 3 = y$ $x + \frac{2}{y} = 0$

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

Solve the simultaneous equations
$ \;\:\: 2x + 5y = 2$ $4x^2 - 17y^2 = 16$

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

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

There is a fraction. By letting the numerator be $x$ and the denominator be $y$, answer the following questions.
<ol class="abc-list"><li><div class="list-item-paragraph">If&nbsp;$4$ is added to the numerator and $5$ is added to the denominator, the new fraction is equivalent to $\frac{3}{4}$. Form an equation based on the information given and show that the equation reduces to $4x-3y=-1$. </div></li><li><div class="list-item-paragraph">If&nbsp;$1$ is subtracted from the numerator and the denominator is multiplied by $4$ the new fraction is equivalent to $\frac{1}{12}$. Form an equation based on the information given and show that the equation reduces to $3x-y=3$. </div></li><li><div class="list-item-paragraph">Hence, solve the simultaneous linear equations and write down the original fraction.</div></li></ol>

There is a fraction.  By letting the numerator be $x$ and the denominator be $y$, answer the following questions.

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