How many solutions does the system of equations have ?

y=-2x+12 and 4y+x-20=0
A. No solution
B. Infinitely many solutions
C. One solution
D. Two solutions

1 answer

To find the number of solutions, we can solve the system of equations using one of the methods such as substitution or elimination.

Using the first equation, we can solve for x in terms of y:
y = -2x + 12
2x = 12 - y
x = (12 - y)/2

Substituting this expression for x in the second equation, we have:
4y + ((12 - y)/2) - 20 = 0

Multiplying both sides of the equation by 2 to eliminate the fraction, we get:
8y + 12 - y - 40 = 0
7y - 28 = 0
7y = 28
y = 4

Substituting this value of y back into the first equation:
x = (12 - 4)/2
x = 8/2
x = 4

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