Question

Use substitution to solve the linear system of equations.
{5x - y = 15
{-10x + 2y = -30

infinitely many solutions
(-15, -6)
(-3,10)
no solution

Answer 1

Solve 5x - y = 15 for y: y = 5x - 15.
Substitute into -10x + 2y = -30:

-10x + 2(5x - 15) = -10x + 10x - 30 = -30,

which is an identity (true for all x). Thus the equations are dependent and there are infinitely many solutions (all points (x, 5x - 15)).