How many solutions does the system of equations have?

Question

y=−2x+12

4y+x−20=0

(1 point)
Responses

Infinitely many solutions
Infinitely many solutions

One solution
One solution

No solution
No solution

Two solutions

Answer 1

The system of equations can be solved by substitution or elimination method.

Using the substitution method:
From the first equation, we have y = -2x + 12.
Substituting this into the second equation, we get:
4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0
-7x = -28
x = 4

Substituting the value of x into the first equation, we get:
y = -2(4) + 12
y = -8 + 12
y = 4

So, the solution to the system of equations is x = 4 and y = 4.

Therefore, the system of equations has one solution.