How do you solve the following system?: 5x + 2y =1 , -8x+3y=12

1 Answer
Jun 23, 2017

(-21/31, 68/31)

Explanation:

5x+2y=1
-8x+3y=12

The best way to solve this system of equations is by using the elimination method. Basically, we need to eliminate a variable by adding the two equations together.

However, to completely cancel out a variable, such as x, they need to have the same coefficient but different signs (positive and negative).

8(5x+2y)=(1)8
5(-8x+3y)=(12)5

40x+16y=8
-40x+15y=60

By multiplying the equations, we can now safely eliminate x from the system by adding the two equations together.

31y=68

y=68/31

Now, you have to plug y back into one of the equations to get x.

5x+2(68/31)=1

5x+136/31=1

5x=1-136/31

5x=-105/31

x=-105/31 * 1/5

x=-21/31

Here's your answer:

(-21/31, 68/31)