how many solutions does the system of equations have?

Question

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

one solution
no solution
two solution
infinitely many solutions

Answer 1

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

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

Let's solve for x in the first equation and substitute it into the second equation:

1) y = -2x + 12
2x = 12 - y
x = 6 - 0.5y

Now substitute this value of x into the second equation:

2) 4y + (6 - 0.5y) - 20 = 0
3.5y - 14 = 0
3.5y = 14
y = 4

Substitute y = 4 back into the first equation to find x:

1) 4 = -2x + 12
-2x = 4 - 12
-2x = -8
x = 4

Therefore, the system of equations has one solution: (4, 4).