How many solutions does the system of equations have? y=−2x+12 4y+x−20=0 (1 point) Responses One solution One solution No solution No solution Infinitely many solutions Infinitely many solutions Two solutions

Answer 1

To solve the system of equations, we can substitute the expression for y in the second equation with -2x + 12:

4(-2x + 12) + x - 20 = 0

-8x + 48 + x - 20 = 0

-7x + 28 = 0

-7x = -28

x = 4

Substituting this value back into the first equation to solve for y:

y = -2(4) + 12

y = -8 + 12

y = 4

Therefore, the system of equations has one solution: x = 4 and y = 4.