Question

How do you solve the following linear system: `-7x - 5y =4, -x + y = 21`?

Answer 1

`x = 101/12`,

`y = 353/12`.

Explanation:

We start with:
`- 7x - 5y = 4`,
`- x + y = 21`.

There are three ways of solving these problems. I'll choose substitution, as I find it easier. Let's start. First of all, we leave `x` or `y` alone in any of the `2` equations. So,
`-x + y = 21`,
`y = x + 21`.

We now substitute this into the other equation:
`- 7x - 5(x + 21) = 4`,
`- 7x -5x + 105 = 4`,
`- 12x = -101`, Which we can write as:
`12x = 101`
`x = 101/12`.

We now substitute this into any of the equation. I'll choose the second one:

`- 101/12 + y = 21`,
`y = 21 + 101/12`
`y = 353/12`.