Edexcel IGCSE Math A Foundation 2.6 Simultaneous Linear Equations Questions

Practise solving pairs of linear equations algebraically or graphically and interpreting their common solution in context.

Exam points

scale equations where needed, then add or subtract to eliminate one variable
substitute the first solution back into either equation to find the second variable
draw both straight lines accurately and read their intersection as the common solution

Covered syllabus points

2.6.A Exact solutions of simultaneous linear equations

[Maximum number: 3]

Solve the simultaneous equations

\begin{aligned} & 5 x+y=11 \\ & 3 x-y=9 \end{aligned}

Show clear algebraic working.

\begin{aligned} & x= \\ & y= \end{aligned}

Working:
5x+y=113x-y=9
Adding:
$8x=20,\qquad x=2.5$ $5(2.5)+y=11,\qquad y=-1.5$

Final answer:
$x=2.5,\qquad y=-1.5$

M1 for a correct elimination or substitution method. M1 dep for finding the second variable. A1 dep on M1 for x=2.5, y=-1.5. Working required.

[Maximum number: 4]

Solve the simultaneous equations

\begin{aligned} & 3 x+2 y=10 \\ & 3 x-4 y=16 \end{aligned}

Show clear algebraic working.

\begin{aligned} & x= \\ & y= \end{aligned}

$3x+2y=10,\qquad 3x-4y=16$
Subtract the second equation from the first:
$6y=-6\quad\Rightarrow\quad y=-1$
Substitute:
$3x+2(-1)=10\quad\Rightarrow\quad x=4$

Final answer:
$x=4,\qquad y=-1$

M1 for a correct elimination/substitution method. M1dep for finding the second variable. A1dep.

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Covered syllabus points

Question 1

Question 2