# Solving a system of equations

#### Eddyrodriguez

So the question is Solve for the system of equations:

y =3x - 10 (-4,-2)

4x-3y=-19
2x+y=13

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#### HallsofIvy

MHF Helper
You have copied (and high-lighted) the last line of problem #10 as if it were part of problem #11. Did you realize that? Problem #11 asks you to solve the two equations 4x- 3y= -19 and 2x+ y= 13. Multiply the second equation by 3, 6x+ 3y= 39, and add that to the first equation.

#### Eddyrodriguez

Thank you I didn’t catch that error but that would’ve simplified everything! I appreciate the help, thank you once again

#### Eddyrodriguez

Where did the 3 come from though like why multiply by 3?

#### SlipEternal

MHF Helper
Where did the 3 come from though like why multiply by 3?
That technique is trying to eliminate one of the variables. So, the first equation has -3y. The second equation has y. If you multiply the second equation by 3, you have a -3y in the first equation and a +3y in the modified second equation, so now when you add them, you have 0y (this gives an equation only in x).

Another method: In the second equation, solve for y in terms of x (I choose the second equation because the coefficient of y is 1):

$y = 13-2x$

Now, plug that into the first equation:

$4x-3(13-2x)=-19$

After multiplying out, you can solve for $x$ since it is an equation in one variable. Once you know x, plug it into the formula you just created for y.

#### DenisB

Where did the 3 come from though like why multiply by 3?
4x-3y=-19 
2x+y=13 

Multiply  by 3 and you now have:
4x-3y=-19 
6x+3y= 39 

4x-3y=-19 
6x+3y=39 
-----------------
10x + 0 = 20
So x = 2

Are you saying that your teacher never taught that?

#### HallsofIvy

MHF Helper
Where did the 3 come from though like why multiply by 3?
The first equation had "-3y". The second equation had "+ y". Multiplying the second equation by 3 changes that to "+ 3y" and adding "-3y+ 3y" eliminates "y" from the equation.