Question

Lukas graphed the system of equations shown.

2x + 3y = 2
y = A system of equations. 2 x plus 3 y equals 2. y equals StartFraction one-half EndFraction x plus 3.x + 3

A coordinate grid with 2 lines. The first line passes through the points labeled (negative 2, 2), (0, 0.67) and (1, 0). The second line passes through the points labeled (negative 2, 2) and (0, 3).
What is the solution to the system of equations?

(–2, 2)
(0, 0.67)
(0, 3)
(1, 0)

Answer 1

The lines intersect at (-2, 2).

Check: Substitute y = 1/2 x + 3 into 2x + 3y = 2:
2x + 3(1/2 x + 3) = 2x + 3/2 x + 9 = (7/2)x + 9 = 2 ⇒ (7/2)x = -7 ⇒ x = -2, y = 1/2(-2)+3 = 2.