Question

Use the substitution method to solve the system x−2y=3
, 4x−8y=12
.(1 point)
Responses

no solution
no solution

(3,0)
left parenthesis 3 comma 0 right parenthesis

infinite solutions
infinite solutions

(0,3)

Answer 1

Infinite solutions.

From x − 2y = 3, x = 2y + 3. Substitute into 4x − 8y:
4(2y + 3) − 8y = 8y + 12 − 8y = 12, which is always true.

So every (x,y) with x = 2y + 3 is a solution, e.g. (2t+3, t) for any real t.