Question

which choice best describes the solution of the system of equations
-24x+8y=24
-15x+5y=15

a many solutions

b (-1,0) is the only soultion
c no soultion

d (1,48) is the only solution

Answer 1

A.

Answer 2

These are both equations of lines, therefore they only intersect at one point.

The first equation can be arranged as y = 3 - 3x and then substituted into the second equation to give -15x +5(3 - 3x) = 15
-> -15x + 15 - 15x = 15
-> -30x = 30
-> x=-1.

So without substituting back in, we know that given x = -1 at the intersection that b is the correct answer.