Question

Solving a System of Equations Using Linear Combination

Answer 1

The solution is (x, y) = (-2, 3)

Solution:

Given system of equations are:

4x + 5y = 7 ------ eqn 1

3x -2y = -12 ------- eqn 2

Multiply eqn 1 by 2

8x + 10y = 14 ------ eqn 3

Multiply eqn 2 by 5

15x - 10y = -60 ------- eqn 4

Add eqn 3 and eqn 4

8x + 10y = 14

15x - 10y = -60

( + ) -------------

23x = -46

x = -2

Substitute x = -2 in eqn 1

4(-2) + 5y = 7

-8 + 5y = 7

5y = 15

y = 3

Thus the solution is (x, y) = (-2, 3)