How do you solve this system by elimination?

Question

-7x-3y=28

-4x-5y=-7

Answer 1

Hi Juliana,

 

Both equations are given in Standard Form, so it is easy to align x-terms and y-terms.  To eliminate one of the terms in the system of equations, we make the coefficient the same (or opposite) and subtract (or add).

 

-7x   -3y   =   28        [eq1]
-4x   -5y   =    -7        [eq2]

 

Choose the variable to eliminate and multiply one (or both) equations by a constant(s).  Let's eliminate x to solve for y.

    -28x   - 12y   =  112          [4*eq1]

   +28x  + 35y   =    49          [(-7)*eq2]

 ---------------------------    [elimination; add equations]

               23y    =  161

                  y     =   7       [divide both sides by 13;  eq3]

 

                3y     =  21         [3*eq3]

    -7x    -  3y     =  28         [eq1]

 --------------------------      [elimination; add equations]

    -7x                = 49

       x                =  -7         [divide both sides by (-7)]

Answer 2

Hi Andrew,

Step One: Get the y terms to equal each other

(-7x-3y=28)5
(-4x-5y=-7)-3

 

-35x-15y=140

12x+15y=28 

Step Two: Eliminate the opposite terms 

-35x-15y+12x+15y=140+28 Rearrange

-35x+12x+15y-15y=161 Combine Like Terms

-23x=161 Divide both side by -23

x=-7

Step Three: Find Y

-4(-7)-5y=-7 

28-5y=-7 

28-5y+7=0 Add 7 to both sides

28+7=5y 

35=5y Divide both sides by 5

y=7

∴x=-7 while y=7

Best, 

Starlyte H.

Answer 3

-7x - 3y = 28

-4x - 5y = -7

 

You need to eliminate one variable.

If we mutiply the 1st equation by -5 and

the 2nd equation by 3 then we will have

15y in equation 1 and -15y in equation 2.

Then add the equations and solve for x

 

-5(-7x - 3y) = -5(28)

3(-4x - 5y) = 3(-7)

 

35x + 15y = -140

-12x - 15y = -21

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

23x + 0y = -161

 

x = -161/23

x = -7

 

Plug -7 in for x in either of the original equations

and solve for y

 

-7(-7) - 3y = 28

49 - 3y = 28

-3y = -21

y = 7

 

x = -7, y = 7

 

Check your answers:

-7(-7) - 3(7) = 28

49 -21 = 28

28 = 28

 

-4(-7) - 5(7) = -7

28 - 35 = -7

-7 = -7

 

Both original equations balance