You can
put this solution on YOUR website!To solve a system of equations by substitution you first need to take one of the equations and set it equal to one of the variables.
Lets take the equation x + y = -9 and set it equal to x
x + y = -9
move y to right side of the equal sign by subtracting it from both sides
x + y - y = -9 - y
y's on the left side cancel out leaving
x = -9 - y
Now that we have shown that x is equal to (-9 - y) we can substitute that value for x in the first equation 3x - y = -7 and solve for y
lets do it.
3x - y = -7
3(-9 - y) - y = -7
multiply 3 across (-9 - y)
-27 - 3y - y = -7
combine like terms
-27 - 4y = -7
move 27 to right side of the equation by add it to both sides
-27 + 27 - 4y = -7 + 27
-4y = -7 + 27
-4y = 20
solve for y by dividing both sides by -4
-4y/-4 = 20/-4
y = -5
So now we have a solution for y. We can use this in either equation to solve for x.
Lets use x + y = -9
x + y = -9
substitute -5 for y
x + (-5) = -9
x - 5 = -9
x - 5 + 5 = -9 + 5
x = -9 + 5
x = -4
Answer: So the solutions are x = -4 and y = -5
Check both of these by trying them in both orginal equations
3x – y = –7
3(-4) – (-5) = –7
-12 + 5 = -7
-7 = -7
----------------------
x + y = -9
(-4) + (-5) = -9
-4 - 5 = -9
-9 = -9
