Question

How do you solve the following system?: `x +3y =8 , 6x +4y = -3`

Answer 1

The values `x=-2 13/14` , `y=3 9/14` fulfills both equations.

Explanation:

It is always helpful to start with drawing the two equations as graphs in a diagram, not least as a check that our solution makes sense:

We want to find a value of x and y which fulfill both equations at the same time, i.e. it must be on both lines f and g on the figure above.

As `x+3y=8`, it follows that
(1) `x=-3y+8`

Insert this value for x in the second equation. To make the solution simpler to follow I will write it as `-3=6x+4y`, that is:
`-3=6x+4y=6(-3y+8)+4y`
`-3=-18y+48+4y=-14y+48`

The last expression can be written as
`14y=48+3=51` or `y=51/14=3 9/14`

Insert this in expression (1):
`x=-3y+8=(-3)51/14+8=(-3*51*8*14)/14`
`x=(-153+112)/14=-41/14=-2 13/14`

Our solution, therefore, is
`x=-2 13/14` , `y=3 9/14`

If we convert these two values to decimal numbers, we see that it agrees with our graph.