Question
How many solutions does the system of equations have y=-2x+12, 4y+x-20=0
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Answered by
GPT 3.5
To solve the system of equations, we can use the method of substitution.
First, substitute the value of y from the first equation into the second equation:
4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0
-7x = -28
x = 4
Next, substitute the value of x into the first equation to find y:
y = -2(4) + 12
y = -8 + 12
y = 4
Therefore, the system of equations has one solution, which is x = 4 and y = 4.
First, substitute the value of y from the first equation into the second equation:
4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0
-7x = -28
x = 4
Next, substitute the value of x into the first equation to find y:
y = -2(4) + 12
y = -8 + 12
y = 4
Therefore, the system of equations has one solution, which is x = 4 and y = 4.
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