-2x+5y=34;2x-7y=-50

Question

Solve the system using addition

Answer 1

The Elimination Method uses either addition or subtraction to eliminate one of the variables in two equations.  The coefficients of that variable must be the same (for subtraction) or opposite (for addition).

 

-2x + 5y =  34

 2x  - 7y = -50

-------------------     (elimination; add equationw)

        -2y = -16

          y  = 8           (divide both sides by -2)

 

         7v =  56         (multiply y=8 by 7 so we can eliminate y]

 2x  - 7y = -50

------------------      (elimination; add equations)

 2x         =    6

   x         =    3       (divide both sides by 2)

 

Checking (very important):

  Is   -2(3) + 5(8) = 34   ?

         -6     +   40    = 34   ?

                34   =   34   ? yes

  Is   (2)(3) -7(8) = -50   ?

          6   -   56  = -50   ?

             -50  = -50   ? yes

Answer 2

Line the equations up vertically, putting x's in one column, y's in another column, and numbers in another column:

 

-2x + 5y =  34

 2x  - 7y = -50

 

Do you see two terms in a column that can be added to make 0? [This is also called solving by elimination.] How about -2x and 2x? Add the two equations, column by column, to make a third equation:

 

   -2x + 5y = 34
+  2x - 7y = -50

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

     0  - 2y = -16

 

Your third equation: -2y = -16. Solve it for y.

If you divide both sides by -2, you get [y = 8].

 

Then, you can plug in 8 for y, in either of the two original equations. I'll use the first one:

 

-2x + 5(8) = 34

-2x + 40 = 34

-2x = -6

 

Solve the equation to get x. If you divide both sides by -2, you get [x = 3].

 

To check your work, plug in 3 for x and 8 for y, in both of the two original equations:

 

-2(3) + 5(8) = 34

(-6) + 40 = 34

34 = 34 [CORRECT]

2(3) - 7(8) = -50

6 - 56 = -50

-50 = -50 [CORRECT]