1. A5 Simultaneous equations
KS4 Mathematics
A5 Simultaneous equations

2. A5.1 Solving simultaneous equations graphically
Contents
A5 Simultaneous equations A
A5.1 Solving simultaneous equations graphically

3. Simultaneous equations
Equations in two unknowns have an infinite number of solution pairs. For example,
x + y = 3
is true when
x = and y = 2
x = and y = 0
x = –2 and y = and so on … 3 x y
x + y = 3
We can represent the set of solutions on a graph:
Ask pupils to suggest other pairs of values that would solve this equation. Praise correct answers involving negative or fractional solutions.
Verify that all of the suggested solutions lie on the line x + y = 3.

4. Simultaneous equations
Another equation in two unknowns will also have an infinite number of solution pairs. For example,
y – x = 1
is true when
x = 1 and y = 2
x = 3 and y = 4
x = –2 and y = –1 and so on … x y 3
y – x = 1
This set of solutions can also be represented in a graph:
Ask pupils to suggest other pairs of values that would solve this equation. Praise correct answers involving negative or fractional solutions.