How do you solve this system by elimination?

Question

x-4y=19

-4x+8y=-28

 

 

 

How do I solve this ? step by step please 

Answer 1

Hi Juliana,

To solve by elimination, we add the 2 equations given together in a way that eliminates one of the variables.

We have 2 equations:

x-4y=19
-4x+8y=-28

We need to rearrange one of them so that the variables cancel out.  Lets start with x.

the first equation has a value of x while the second has -4x.  For these  to cancel out, we either need to multiply the top equation by 4 or divide the bottom equation by 4.  

Lets divide both sides the bottom equation by 4:

(-4x+8y)/4 = -28/4

 

-x+2y=-7

Now we add the original first equation to the modified second equation:

 

 x-4y=19

-x+2y=-7

Add both sides of the equation to one another:

x-4y-x+2y=19-7

simplify to get -2y=12

divide both sides by -2

y=-6

Then use either equation to solve for x:

x-4y=19

x-(4*-6)=19

x+24=19

x=-5

So x=-5 and y=-6.

 

For the sake of example, lets solve this equation by eliminating y now.

x-4y=19
-4x+8y=-28

We can divide both sides of the lower equation by 2 to get:

-2x+4y=-14

 

Then we add the 2 equations together:

     x-4y=19

+ -2x+4y=-14

= -x=5

x=-5

Use either equation to solve for y:

x-4y=19

(-5)-4y=19

-4y=24

y=-6

so x=-5 and y=-6

 

Hope this helps!

Message me if you have any questions.

Thanks!

Beth