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SIMULTANEOUS EQUATIONS 1
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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.
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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.
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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.
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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.
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