1. SIMULTANEOUS EQUATIONS 1

2. Solving simultaneous equations graphically
Solve the simultaneous equations and x y 4 2 -2 -4 x 1 2 y x 1 2 y -2 × × × × x 1 2 y 3 x 1 2 y × ×
The lines intersect at the point (3, 4).
So x = 3 and y = 4.

3. Solving simultaneous equations using the elimination method
1 Solve the simultaneous equations and
(1)
(2)
Equation (1) – equation (2)
Substitute x = 5 in equation (1) and then solve to find y.
Check:
(3 × 5) + (2 × 1) = 17
5 + (2 × 1) = 7
The solution is x = 5 and y = 1.

4. 2 Solve the simultaneous equations and
(1)
(2)
Equation (1) + equation (2)
Substitute x = 3 in equation (2) and then solve to find y.
Check:
(3 × 3) − (4 × 2) = 1
(2 × 3) + (4 × 2) = 14
The solution is x = 3 and y = 2.

5. 3 Solve the simultaneous equations and
(1) multiply by 2
(2) multiply by 3
(3)
(4)
Equation (3) + equation (4)
Substitute x = 4 in equation (1) and then solve to find y.
Check:
(2 × 4) + (3 × -1) = 5
(5 × 4) − (2 × -1) = 22
The solution is x = 4 and y = −1.