solve by substitution method:
8x-3y=-94
2x+22=y
8x-3y=-94
2x+22=y
8x - 3(2x + 22) = -94
8x - 6x + 66 = -94
2x = -94 - 66
2x = -160
x = - 80
Take it from there.
To solve the given system of equations by the substitution method, we will substitute the value of "y" from the second equation into the first equation.
Given equations:
1) 8x - 3y = -94
2) 2x + 22 = y
Step 1: Convert the second equation into the form "y = ...".
We rearrange equation 2 to isolate "y":
2x + 22 = y
Subtract 22 from both sides:
2x = y - 22
Step 2: Substitute the value of "y" from equation 2 into equation 1.
Replace "y" in equation 1 with (y - 22). The modified equation becomes:
8x - 3(y - 22) = -94
Step 3: Simplify and solve for "x".
Distribute the -3 across the parentheses:
8x - 3y + 66 = -94
Rearrange the equation:
8x - 3y = -94 - 66
Combine like terms:
8x - 3y = -160
Step 4: Solve for "x".
We have obtained a new equation: 8x - 3y = -160.
Now, we can solve for "x".
To do this, we need to isolate "x" by moving -3y to the other side.
8x = -160 + 3y
Step 5: Solve for "x" continued.
Now substitute the value of y from equation 2 into equation 3:
8x = -160 + 3(2x + 22)
8x = -160 + 6x + 66
8x - 6x = -160 + 66
2x = -94
Divide both sides of the equation by 2:
2x/2 = -94/2
x = -47
Step 6: Substitute the value of "x" into equation 2 to find the value of "y".
2(-47) + 22 = y
-94 + 22 = y
-72 = y
So, the solution to the system of equations is:
x = -47
y = -72