Question

How do solve the following linear system?: `-4x + 4 = -4y, 7x + 6y + 11 = 0`?

Answer 1

The solution is `(-5/13, 8/13)`

Explanation:

This problem makes things fairly easy for you by providing a clear definition of `y` in the first equation:

`-4x + 4 = -4y`
`x - 1 = y`

We can plug this into the other equation to solve for `x` and then use it to find `y`:
`7x + 6(x - 1) + 11 = 0`
`7x + 6x - 6 + 11 = 0`
`13x + 5 = 0`
`x = -5/13`

Then:
`-5/13 + 1 = y`
`y = 8/13`

So the solution is `(-5/13, 8/13)`

A little additional info on the problem in concluding. In case it is not clear, the solution takes the form of a point, `(x,y)`. This is because solving a system of equations is the same as finding the point(s) at which those lines (or curves) intersect.