Simultaneous Equations (Edexcel GCSE Maths: Foundation): Exam Questions

Solve the simultaneous equations.
You must show all your working.

$\begin{array}{rcl}x+3y& =& 19\\ -2x+4y& =& 32\end{array}$

$$\begin{gathered} x=...................................... \\ y=...................................... \end{gathered}$$

Use substitution to solve the simultaneous equations.
You must show all your working.

$\begin{array}{rcl}2x-5y& =& 32\\ y& =& 14-3x\end{array}$

$$\begin{gathered} x=.......................... \\ y=.......................... \end{gathered}$$

Use the graphs to solve the simultaneous equations

$\begin{array}{rcl}4x+2y& =& 8\\ y& =& x+1\end{array}$

$$\begin{gathered} x=.......................... \\ y=.......................... \end{gathered}$$

Solve the simultaneous equations.
You must show all your working.

$\begin{array}{rcl}3x-8y& =& 22\\ x+4y& =& 4\end{array}$

$$\begin{gathered} x=...................................... \\ y=...................................... \end{gathered}$$

Solve the simultaneous equations.
You must show all your working.

                  $\begin{array}{rcl}3x-y& =& 22\\ x+2y& =& 5\end{array}$

$$\begin{gathered} x=................................................... \\ y=................................................... \end{gathered}$$

Solve the simultaneous equations.

You must show all your working.

$$\begin{gathered} 5x-2y=26 \\ 7x+6y=10 \end{gathered}$$

$x=$............................ 

$y=$............................ 

Solve the simultaneous equations

$$\begin{gathered} 3x+y=12 \\ x-5y=20 \end{gathered}$$

Solve the simultaneous equations.
You must show all your working.

$\begin{array}{rcl}5x-9y& =& 44\\ 11x+3y& =& 17\end{array}$

$$\begin{gathered} x=...................................... \\ y=...................................... \end{gathered}$$

Use substitution to solve the simultaneous equations.
You must show all your working. 

$\begin{array}{rcl}4x-7y& =& 15\\ 2x& =& 3y+6\end{array}$

$$\begin{gathered} x=.......................... \\ y=.......................... \end{gathered}$$

Use the graphs to solve the simultaneous equations

$\begin{array}{rcl}4x+3y& =& 12\\ x-y& =& -2\end{array}$

$$\begin{gathered} x=.......................... \\ y=.......................... \end{gathered}$$

Solve the simultaneous equations.

You must show all your working.

$\begin{array}{rcl}5x+4y& =& 10\\ 7x-6y& =& 43\end{array}$

$$\begin{gathered} x=................................................... \\ y=................................................... \end{gathered}$$

Solve the simultaneous equations.
You must show all your working.

$\begin{array}{rcl}5x-2y& =& 44\\ 2x+3y& =& 10\end{array}$

$\begin{array}{rcl}x& =& .................................................\\ y& =& .................................................\end{array}$

The equations of two straight lines are $y=3x+13$ and $y=7x-3$.

Use algebra to solve these two simultaneous equations to find the co-ordinates of the point where the lines meet.
You must show all your working.

A sweet shop sells two different types of sweets, Apple sours ($a$ grams) and Bonbons ($b$ grams).

3 apple sours and 4 bonbons are put on some scales and they are balanced with a block weighing 37 grams.

2 apple sours are put on some scales and they are balanced with 3 bonbons and a block weighing 2 grams.

Use the weight scales to calculate the mass in grams of each type of sweet purchased.