SOLUTION: 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,

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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