Question

y = –A system of equations. y equals negative StartFraction one-half EndFraction x plus 4. x plus 2 y equals negative 8.x + 4
x + 2y = –8
How many solutions does this linear system have?

one solution: (8, 0)
one solution: (0, 8)
no solution
infinite number of solutions

Answer 1

No solution.

Substitute y = -1/2 x + 4 into x + 2y = -8:
x + 2(-1/2 x + 4) = x - x + 8 = 8, which contradicts x + 2y = -8.
The two lines have the same slope (-1/2) but different intercepts (4 and -4), so they are parallel and never meet.