How many solutions does the system of equations have?y=−2x+12 4y+x−20=0 (1 point)ResponsesNo solutionNo solutionTwo solutionsTwo solutionsInfinitely many solutionsInfinitely many solutionsOne solution

Answer 1

The system of equations is:

y = -2x + 12
4y + x - 20 = 0

To find the number of solutions, we can solve the system of equations.

Rearranging the second equation, we have:

x = 20 - 4y

Substituting this value for x in the first equation:

y = -2(20 - 4y) + 12
y = -40 + 8y + 12
-7y = -28
y = 4

Substituting y = 4 into the second equation:

4(4) + x - 20 = 0
16 + x - 20 = 0
x - 4 = 0
x = 4

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

The correct response is:

One solution