SOLUTION: The problem says solve by substitution to find the solution of 5x+5y=-20 and -9x+y=76 there may not be a solution as well but that is where I get confused.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: The problem says solve by substitution to find the solution of 5x+5y=-20 and -9x+y=76 there may not be a solution as well but that is where I get confused.      Log On


   

Question 372417: The problem says solve by substitution
to find the solution of
5x+5y=-20
and -9x+y=76
there may not be a solution as well but that is where I get confused.
Answer by marcsam823(57) About Me  (Show Source):
You can put this solution on YOUR website!
5x +5y = -20
-9x + y = 76
To solve by substitution solve one equation for one variable and substitute that value into the second. There are several ways to do this with problems of this type.
Let's start with:
5x+%2B+5y+=+-20
Divide each term by 5:
5x%2F5+%2B+5y%2F5+=-20%2F5
x+%2B+y+=+-4
We can now easily solve for x or y. Let's solve for y by subtracting x from both sides of the equation:
y+=+-x+-4
In the second equation, substitute -x-4 for y
-9x+%2B+y+=76
-9x+%2B+%28-x+-4%29+=76
Now we have only one variable (x) and can solve for it.
Combine like terms:
-10x+-+4+=+76
Add 4 to both sides of the equation:
-10x+=+80
Solve for x by dividing both sides by -10
x+=+-8
To solve for y, plug x = -8 into either one of the original equations.
5x+%2B+5y+=+-20
5%28-8%29+%2B+5y+=+-20
-40+%2B+5y+=+-20
5y+=+20
y+=+4
To further verify that x = -8 and y = 4, check by substituting these values into the other equation.
-9x+%2B+y+=+76
-9%28-8%29+%2B+4+=+76
72+%2B+4+=+76
76+=+76
The correct answers are x+=+-8 and y+=+4
There will be instances where there is no solution. If you solve for x and y in the first equation and the results do not fit into the second, then there is no solution. Be aware that your textbook may present you with a problem like that.