System of equations by substitution
We want to know if there is any form for both equations to have the same x and y
-4x + y = 13
-5x + 8y = -4
Step 1: we find an expression for y
We solve one of the equations for x or y. In this case we are solving the first for y:
-4x + y = 13
↓ taking -4x to the right side
y = 13 + 4x
Step 2: finding an equation with just one unkown, x
In order to find an equation with just one unkown we replace y = 13 + 4x
on the other equation, the second equation:
-5x + 8y = -4
↓ replacing y by 13 + 4x
-5x + 8(13 + 4x) = -4
↓ since 8(13 + 4x) = 104 + 32x
-5x + 104 + 32x = -4
↓ since -5x + 32x = 27x
104 + 27x = -4
Step 3: finding x
Using the equation found we are going to find x
104 + 27x = -4
↓ taking 104 to the right side
27x = -4 - 104
↓ since -4 - 104 = -108
27x = -108
↓ taking 27 to the right side
x = -108/27
↓ since -108/27 = -4
x = -4
Step 4: finding y
Now, we just replace the value for x we found in any of the equations (we must have the same result on both):
in the first equation...
-4x + y = 13
↓ replacing x = -4
-4(-4) + y = 13
↓ since -4(-4) = 16
16 + y = 13
↓ taking 16 to the right side
y = 13 - 16 = -3
Then, the solution is when x = -4 and y = -3
Answer: (-4, -3)