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x-4y=11-3x+12y+6

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2 Answers

Hi, Christina.

Did you intend to write an = sign before the 6?
If so, then here's how you go about solving this system using substitution:

x - 4y =11
-3x +12y = 6

The idea behind substitution is to get one variable by itself (that is, solve for one of the variables) and then using its expression in the other equation.  Let me explain by doing...

The top equation looks like an easy one to get x alone...

x - 4y = 11
  +4y     +4y                                                        .
x     = 4y + 11

Now take the expression (4y + 11) and put it into x's place in the other (bottom) equation:

-3x  + 12y = 6
-3(4y + 11)  + 12y = 6

Simplify the left side of the equation and then proceed to solve for y:

-3(4y + 11) + 12y = 6
-12y   -  33  + 12y  = 6
        - 33            =  6

Since  -33 will never = +6, we say that these lines are parallel and do not have a solution.

Hope this helped.  
If this is not the problem you were trying to solve, let me know, and we can try the intended problem together.

Christina, you have two variables, x and y, but only one equation.  You cannot solve for both x and y unless you have a second equation.

You can simplify the equation that you have, a bit:

x - 4y = 17 - 3x + 12y  (combine the constants)

x = 17 - 3x + 16y  (add 4y to both sides)

4x = 17 + 16y  (add 3x to both sides)

x = 17/4 + 4y  (divide both sides by 4)

But as you can see, you still have to know y to solve for x, or vice versa.

Do you have a second equation that you're not showing us?