Question

How do solve the following linear system?: `-x+5y=-5 , -7x+y=-19`?

Answer 1

`x = 45/17` and `y = -8/17`

Explanation:

There are several methods to solve simultaneous equations:

Substitution, elimination, or by equating two variables.

Let's make y the subject in both equations:

Equ 1: `5y = x - 5" Equ 2": y = 7x - 19`
`" " y = x/5 - 1`

The two y values are equal: y = y
Therefore: `x/5 - 1 = 7x - 19 " " xx 5`

`x - 5 = 35x - 95 " solve for "x`
`90 = 34x`
`90/34 = x rArr " "x = 45/17`

Now that we have the value for x, substitute into both equations to check the value for y.

`y = 45/17 ÷ 5 - 1` and `y = 7 (45/17) - 19`
`y = -8/17 " "y = -8/17`