Linear System formula?? Every time I try substitution I end up with a fraction?

Question

Does anyone know how to solve this problem? I know there's a formula but I don't get my book until Monday and this is due tomorrow.

solve the linear system

4x - 3y = -19

3x + 2y = 24

Answer 1

You add the two equations together, I believe. You would either end up with 7x - y = 5, OR you can multiply one of the equations so that either the y's are opposites or the x's are opposites. Then you could solve for y and substitute.

-y = -7x + 5

y = 7x -5

3x + 2(7x - 5) = 24

3x + 14x -10 = 24

17x = 34

x = 2

Now you can solve for y on your own. If you get a fraction, go back and check it. Then get another person to check it, if possible. Sometimes you are blind to little mistakes. Oh... except it isn't a fraction. I just solved for y. if its a whole number higher than two, you probably got it right. That's all I'm going to say--the rest is up to you!

Good luck!

Answer 2

Yes. You do get fraction and but the question seems to be wrong.

Is it +19 instead of -19 ??

If its +19 then you can get whole numbers. x=10 y=7

Anyway do double check your question.

Answer 3

Not as hard as it seems...

First pick an equation and get the x on one side and the y on the other.  I started with the second.

x=(24-2y)/3

Now that you know what x equals, plug that back into your first equation.

4((24-2y)/3)-3y=-19

Solve for y, y=9

Plug 9 into the first equation to get 4x-3(9)=-19

Solve for x, x=2

P.S. since you're making your equations equal, it doesn't matter which one you start with or which one you plug your answers back into...

Answer 4

multiply both formulas until they cancel out one variable when added together

8x-6y=-38

9x+6y=72

---------------

17x+0y=34

x=2

Therefore

8-3y=-19

-3y=-27

y=9

To prove it

6+2y=24

2y=18

y=9 again

Answer 5

     4x - 3y = -19

-   3x + 2y = 24

_________________

     x - 5y = -45

           x = -45 - 5y

4(-45 - 5y) - 3y = -19

-180 - 20y - 3y = -19

               -23y = 161

                    y = -7

                    x = -45 - 5(-7)

                    x = -45 + 35

                    x = -10

answer is: x = -10

                y = -7

Answer 6

You have to multiply each equation by a number to get rid of one of the variables.

2(4x - 3y) = 2(-19)

3(3x + 2y) = 3(24)

That will give you

8x - 6y = -38

9x + 6y = 72

When you add the equations together the y's cancel.

17x = 34

x = 2

Plug that back in to one of the equations

y = 9