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Question 335143: In an substitution problem, when you have two variables on one side of the equal sign, what do I do?
Here is the problem:
3x - y = 5
-4x + 2y = -6
I know it is dependent, but I don't know how to get there! I did the other day... but now can't remember and have my final tomorrow.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! You have 2 equations in 2 unknowns.
You want to substitute for one of the variables to get one equation in one unknown.
At least that's what I think you're asking.
Take the first equation and solve for x or y.
We'll do y.
You start with 3x - y = 5
Add y to both sides of this equation and subtract 5 from both sides of this equation to get:
y = 3x - 5
Substitute for y in the second equation.
The second equation is -4x + 2y = -6
Substitute for y in the second equation by the value of y that you solved for in the first equation to get:
-4x + 2 * (3x-5) = -6
Simplify this by multiplying out the factors to get:
-4x + 6x - 10 = -6
Add 10 to both sides of this equation and combine like terms to get:
2x = 4
Divide both sides of this equation by 2 to get:
x = 2
Now that you know the value of x, you can solve for y in either of the original 2 equations.
From the first equation, you have 3x - y = 5
Substitute for x in this equation to get:
3*2 - y = 5 which becomes:
6 - y = 5
Subtract 6 from both sides of this equation to get:
-y = -1
Multiply both sides of this equation by -1 to get:
y = 1
You now have:
x = 2 and y = 1
Substitute in both original equations to see if they are true.
3x - y = 5 becomes 3*2 - 1 = 5 which becomes 6 - 1 = 5 which becomes 5 = 5 which is true.
-4x + 2y = -6 becomes -4*2 + 2*1 = -6 which becomes -8 + 2 = -6 which becomes -6 = -6 which is true.
Both original equations are true, so the values of x = 2 and y = 1 are good.
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