Question

What is the solution of the system? Use elimination. 7x + 5y = 19 −7x − 2y = −16

Answer 1

Make the coefficient of y the same in both equations:

To do this, multiply equation one by 2, and equation two by 5 (this will make the coefficient 10 in both).

14x + 10y = 38
-35x - 10y = -80

Eliminate the y variable by adding the equations from each other

   (14x + 10y = 38)
+ (-35x - 10y = -80)
=  -21x +  0y  = -42

We now have -21x = -42. The y variable has been eliminated.

Solve for x

-21x = -42

Divide both sides by -21 to get x on its own.

x = 2

Substitute x into the equation to find y.

7*2+5y=19

14+5y=19

Subtract 14 from both sides.

5y=19-14

5y=5

Divide by 5 on both sides to get y on its own.

y=5/5

y=1

The answer is (2,1)