Question

How do you solve the system of equations `y=-3x-11` and `y=-2x-8`?

Answer 1

`x =-3 and y =-2`

Explanation:

Notice that both equations represent the equation of straight lines.

By solving them as a system we are actually finding the point of intersection of the two lines.

You have `color(red)(y) = color(blue)(-2x -8)" and " color(red)(y) = color(blue)(-3x -11)`

`color(white)(xxxxxxxxxxxxxxxxx) color(red)(y = y)`

Which then means `color(blue)(-2x -8)= color(blue)(-3x -11)`

`color(white)(xxxxxxxxxx)-2x +3x = -11+8`

`color(white)(xxxxxxxxxx.xxxxxx)x = -3`

Now find `y`

`y = -2(-3)-8`
`y = +6-8`
`y = -2`

Check:
`y= -3(-3)-11`
`y =+9-11`
`y =-2`