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Solve 8x-3y=25 and 12x+5y=9. You must show your working.

Solve $8x-3y=25$ and $12x+5y=9$. You must show your working.

Solving Simultaneous Linear Equations using Elimination Method

2025 YCKSS PRELIMS P1 Q13

Simultaneous Equations

In the figure below, triangle $ABC$ is congruent to triangle $PQR$.
<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/1764913549185-i7am85u012c.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQ5MTM1NDkxODUtaTdhbTg1dTAxMmMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUxMDkxMiwiZXhwIjoxNzkzNTExMjEyfQ.h8gPbly63U1lpfKJnjqhp-iKQAPf4y0zCseUruNmKVQ" style="max-width: min(350px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-paragraph">From the information above, form two simultaneous equations relating the values of $x$ and $y$.</div></li><li><div class="list-item-paragraph">Solve the simultaneous equations in (a) to find the values of $x$ and $y$.</div></li></ol>

In the figure below, triangle $ABC$ is congruent to triangle $PQR$.

Congruence

Congruent Triangles: Setting Up and Solving for $𝑥$ and $𝑦$

Congruence and Similarity

Solve the simultaneous equations by using elimination method.
$\begin{align}
 & \frac{7}{2}w-4=\frac{5y}{3} \\ 
 & 14w-15y=\frac{27}{2} 
\end{align}$

Solve the simultaneous equations by using elimination method.

$\begin{align}
  & \frac{7}{2}w-4=\frac{5y}{3} \\ 
 & 14w-15y=\frac{27}{2}  
\end{align}$


Elimination Method for Linear Equations with Fractions

Solve the simultaneous equations by using elimination method.
$\begin{align}
 & 1.2x-0.5y=1.6 \\ 
 & \frac{2}{5}x+\frac{1}{4}y=2.2 
\end{align}$

$\begin{align}
  & 1.2x-0.5y=1.6 \\ 
 & \frac{2}{5}x+\frac{1}{4}y=2.2  
\end{align}$


Elimination Method for Linear Equations with Fractions/Decimals

Solve the simultaneous equations by using elimination method.
$\begin{align}
 & 3x+5y=5 \\ 
 & \frac{1}{2}x=\frac{1}{3}y+2 
\end{align}$

$\begin{align}
  & 3x+5y=5 \\ 
 & \frac{1}{2}x=\frac{1}{3}y+2  
\end{align}$


Simultaneous Linear Equations (Elimination Approach)

Solve the simultaneous equations by using elimination method.
$\begin{align}
 & 2x+5y=4 \\ 
 & 3x-2y=25 
\end{align}$

$\begin{align}
  & 2x+5y=4 \\ 
 & 3x-2y=25  
\end{align}$


Elimination Method for Solving Linear Equations

Solve the simultaneous equations by using elimination method.
$\begin{align}
 & 2x+3y=2 \\ 
 & 5-4x=9y 
\end{align}$

$\begin{align}
  & 2x+3y=2 \\ 
 & 5-4x=9y  
\end{align}$


Solving Simultaneous Equations by Elimination

By using the elimination method, solve the simultaneous equations.
$\begin{align}
 & 3x+y=4 \\ 
 & 4x+2y=5 
\end{align}$

By using the elimination method, solve the simultaneous equations.

$\begin{align}
  & 3x+y=4 \\ 
 & 4x+2y=5  
\end{align}$


Using Elimination to Solve a System of Equations

By using the elimination method, solve the simultaneous equations.
$\begin{align}
 & 9y+x=10 \\ 
 & 3y-x=2 
\end{align}$

$\begin{align}
  & 9y+x=10 \\ 
 & 3y-x=2  
\end{align}$


Elimination Method for Linear Simultaneous Equations

By using the elimination method, solve the simultaneous equations.
$\begin{align}
 & -5x+y=3 \\ 
 & 4x+3y=47 
\end{align}$

$\begin{align}
  & -5x+y=3 \\ 
 & 4x+3y=47  
\end{align}$


By using the elimination method, solve the simultaneous equations.
$\begin{align}
 & 2x+5y=11 \\ 
 & 2x-6y=0 \\ 
\end{align}$

$\begin{align}
  & 2x+5y=11 \\ 
 & 2x-6y=0 \\ 
\end{align}$


Explain, with mathematical working, why the following pair of simultaneous equations have no solutions.
${2x + 5y = 7}$
${15(y - 1) = -6x}$

Explain, with mathematical working, why the following pair of simultaneous equations have no solutions.

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