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).
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