Question

What is the solution to the system of equations? x-2y=-1 3x-6y=-3

infinitely many solutions
no solution
(-5,1)
(-10,2)

Answer 1

infinitely many solutions

Explanation:

x - 2y = - 1 ( add 2y to both sides )

x = - 1 + 2y → (1)

3x - 6y = - 3 → (2)

substitute x = - 1 + 2y into (2)

3(- 1 + 2y) - 6y = - 3 ← distribute parenthesis and simplify left side

- 3 + 6y - 6y = - 3 ( add 3 to both sides )

6y - 6y = 0

0 = 0 ← true statement

this indicates the system has infinitely many solutions