Question

Use the substitution method to solve the system 2x+3y=4
, −4x−6y=−8
.(1 point)

(−1,2)


(2−1)


infinite solutions

no solution

Answer 1

Solve 2x+3y=4 for x: x = 2 − (3/2)y.
Substitute into −4x−6y=−8: −4(2 − (3/2)y) −6y = −8 → −8 +6y −6y = −8 → −8 = −8 (identity).

The equations are dependent (the second is −2 times the first), so there are infinitely many solutions.
Solution set: {(x,y) | x = 2 − (3/2)y, y any real}.