Question 125103: Will you help me with substitution?
y=4x
3x-y=1
and
-3x+5y=81
2x+y=24
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! I would love to help you with substitution. The idea with substitution is you have 2 equations with 2 variables, and you want to make it 1 equation with 1 variable, so you can solve for that variable. The first system of equations is set up for substitution right away. It says y=4x. That means any time you see y, you can write 4x instead (that is the substituting). So In the second equation, change 3x-y=1 to 3x-(4x)=1. Now solve for x like a regular equation. 3x-4x=1 becomes -x=1, which becomes x=-1.
You can now plug that back into the other equation to find y.
y=4x, so y=4(-1), so y=-4.
So your solution is x=-1, y=-4. Those should work in both equations.
The second system of equations is not set up for substitution as easily. You can set it up by changing one of the equations to x=___ or y=___. I will change the second because that y is alone already, so it will take less steps. Change 2x+y=24 to y=24-2x. Now substitute that "y" into the first equation. Change -3x+5y=81 to -3x+5(24-2x)=81. Distribute the 5 and then solve like before.
-3x+120-10x=81
-13x+120=81
-13x=-39
x=3
Change y=24-2x to y=24-2(3), so y=24-6, so y=18.
So x=3, y=18.
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