Question

For each ordered pair, determine whether it is a solution to the system of equations.
{y=7x-3
{-14x+2y=-6
Is it a solution?
Yes No

Answer 1

Substitute y = 7x − 3 into the second equation:
-14x + 2y = -14x + 2(7x − 3) = -14x + 14x − 6 = −6,
which is true for every x. The second equation simplifies to y = 7x − 3, so both equations are the same line.

Therefore the system is dependent and has infinitely many solutions: an ordered pair is a solution iff it satisfies y = 7x − 3. (For example, (1,4) is a solution since 4 = 7(1) − 3; (0,0) is not since 0 ≠ −3.)