Question

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

Answer 1

`(-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)`