Question 172805: How do i slove the system 2x-5y=9 and -3x+y=-7 using the substitution method?
Answer by colliefan(242)   (Show Source):
You can put this solution on YOUR website! Solve 2x-5y=9 and -3x+y=-7 using the substitution method:
Pick either equation and solve it for one variable, either variable will work. Let's say we're going to solve the second equation for y.
-3x+y=-7
+3x-3x+y=-7+3x
y=3x-7
Now, since y = 3x-7, we can replace y by 3x-7 in the other equation. That is why it is called the substitution method. We are substituting an expression from one equation into the other.
2x-5(3x-7) = 9
2x - 15x + (-5)(-7) = 9
-13x + 35 = 9
-13x= -26
x=2
Now that you know what x is, substitute it back into either equation and solve for y. Again, if you use the second equation:
-3x+y=-7
-3(2)+y = -7
-6 + y = -7
y = -1
The solution we have calculated is x=2 and y=-1. Substitute these values into both equations to check to make sure this is a valid solution to the equations and you will see that this is the solution to these equations.
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