Question

Which of the following systems
describes a zero-solution? (1 point)
6y = −12x + 18 and
8x + 4y = 2
2y + x = 3 and 4x + 8y = 12
y = x + 6 and 1
2 −6 − 2y = x
y = x and y = −x

Answer 1

The first system:
6y = −12x + 18 and 8x + 4y = 2

Rewrite the first as y = −2x + 3. Substitute into 8x + 4y = 2 (or 2x + y = 1/2):
2x + (−2x + 3) = 1/2 ⇒ 3 = 1/2, a contradiction.

So the lines are parallel and there is no solution. (For reference: the second system is the same line twice (infinitely many solutions); y = x and y = −x intersect at (0,0).)