Solve the system of equations
4x - 8y = -36
-6x + y = 32
To solve the system of equations, we can use the method of substitution.
First, let's solve the second equation for y:
-6x + y = 32
y = 6x + 32
Now we can substitute this expression for y into the first equation:
4x - 8y = -36
4x - 8(6x + 32) = -36
4x - 48x - 256 = -36
-44x - 256 = -36
-44x = 220
x = -220/44
x = -5
We can substitute this value of x into the second equation to solve for y:
-6(-5) + y = 32
30 + y = 32
y = 32 - 30
y = 2
Therefore, the solution to the system of equations is x = -5 and y = 2.
To solve the system of equations:
Step 1: Choose a variable to eliminate by multiplying one or both equations by constants that result in the coefficients of either x or y being the same in both equations.
In this case, we can eliminate the y variable by multiplying the second equation by 8:
-6x + y = 32
8(-6x + y) = 8(32)
-48x + 8y = 256
Now our system of equations is:
4x - 8y = -36
-48x + 8y = 256
Step 2: Add the two equations together to eliminate the y variable.
(4x - 8y) + (-48x + 8y) = -36 + 256
-44x = 220
Divide both sides of the equation by -44:
x = -5
Step 3: Substitute the value of x into one of the original equations to solve for y. Let's use the first equation:
4x - 8y = -36
4(-5) - 8y = -36
-20 - 8y = -36
Subtract -20 from both sides of the equation:
-8y = -36 + 20
-8y = -16
Divide both sides of the equation by -8:
y = 2
So the solution to the system of equations is x = -5 and y = 2.