SOLUTION: i dont understand how to do this 7. Solve using substiitution a) y=x-1 y=2x-3 b) x=-2y+3 x=3y-7 8. Solve using substitution a) y=3x-8 5x+y=6 d) 3m-2n=-5

Question 12746: i dont understand how to do this
7. Solve using substiitution
a) y=x-1
y=2x-3
b) x=-2y+3
x=3y-7
8. Solve using substitution
a) y=3x-8
5x+y=6
d) 3m-2n=-5
m=n-2
e) 2a-3b=-4
a=5-2b
i) 2x+y=5
x-3y=13

Answer by glabow(165) (Show Source): You can put this solution on YOUR website!
I'll do one and you do the rest, okay?
Solving by substitution means finding one variable in terms of the other.
Look at a). You have y = x-1. That means you know what y is IN TERMS OF X.
The related equation says y = 2x-3. In this equation you can substitute x-1 for y [that's the substitution part of the method]. So the second equation becomes x-1=2x-3. Since this is just one variable (x) you can rearrange terms and solve for x.
x-1 = 2x-3
x = 2x -2 [adding 1 to both sides]
-x = -2 [adding -2x to both sides]
x = 2 [multiplying both sides by -1]
But y=x-1. So, y = 2-1 = 1. [Substituting 2 for x]
Check: 1 = 2 - 1 [the first equation]
1 = 4 - 3 [the second equation]
Do the same thing with each of the other sets of equations. Just notice in the one marked i) you have to find one of the variables in terms of the other first.
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