Edexcel IGCSE Math A Higher 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 2.6.HA Higher-tier simultaneous linear equations 2.6.HB Graphical interpretation of simultaneous equations

[Maximum number: 3]

Solve the simultaneous equations

$\begin{aligned} 3x+5y&=8\\ 4x+y&=-3.5 \end{aligned}$

Show clear algebraic working.

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

$\begin{aligned} 3x+5y&=8\\ 20x+5y&=-17.5 \end{aligned}$

Subtract:
-17x=-25.5x=-1.5

Substitute:
y=2.5

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

Working required.

[Maximum number: 3]

Here is the graph of the equation 2y+x=1 drawn on a grid.

By drawing another straight line on the grid, solve the simultaneous equations
$\begin{aligned} y-x-2&=0\\ 2y+x&=1 \end{aligned}$ $\begin{aligned} x&=\\ y&= \end{aligned}$

Figure for Question 2 — Edexcel IGCSE Math A Higher

Draw the line
y-x-2=0
or
y=x+2

For example, it goes through:
(-2,0), (-1,1), (0,2), (1,3), (2,4)

Intersection:
$\begin{gathered} x=-1\\ y=1 \end{gathered}$

Marking guidance:
- M1 for drawing the line y=x+2, long enough to see the intercept with the other line
- This question tests using graphs to solve simultaneous equations;
ignore algebraic methods
- A2 for both values correct, dependent on M1;
A1 for one correct value or both values reversed
- If more than one line is drawn, credit a correct line with correct coordinates

[Maximum number: 3]

Solve the simultaneous equations

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

Show clear algebraic working.

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

$5x+y=11,\qquad 3x-y=9$
Add:
$8x=20\quad\Rightarrow\quad x=2.5$
Substitute:
y=11-5(2.5)=-1.5

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

M1 for eliminating one variable or a correct substitution method. M1 for finding the second variable. A1 for both values.

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Covered syllabus points

Question 1

Question 2

Question 3