Question

Use addition to solve the linear system of equations.
{2x + y = 5
{3x + 2y = 4

(6,7)
(6,-7)
(-6,-7)
(-7,6)

Answer 1

Use elimination. Multiply the first equation by -2:
-4x - 2y = -10
Add this to the second equation:
(3x + 2y) + (-4x - 2y) = 4 + (-10) ⇒ -x = -6 ⇒ x = 6.
Substitute into 2x + y = 5:
2(6) + y = 5 ⇒ 12 + y = 5 ⇒ y = -7.

Solution: (6, -7).