Question

How do you solve the following linear system: `y=-x+4, 3x+y=-2`?

Answer 1

`x=-3 and y=7`

Explanation:

This is one of the best forms you can have for a system of equations. Note that they each have a single `y` term...

Graphically it means they each represent a straight line and the solution is the point of intersection of the lines.

Write each equation in slope-intercept form, ie with `y` on one side.

`y = -x+4 " and "y= -3x-2`

Now, as `y = y`, equate the right sides of the equations:

`-x+4 =-3x-2`

`3x-x=-2-4`

`2x = -6`

`x=-3`

Now you can use one equation to find a value for `y` and the
other equation to check.

`y = -(-3)+4" "and" "y =-3(-3)-2`
`y= 3+4color(white)(wwwwwwwwwwww.w)y = 9-2`
`y =7color(white)(wwwwwwwwwwwwwwww)y=7`