Question

How do you find the solution set for y=6x-5 and y=-x+9?

Answer 1

`{(x = 2), (y = 7) :}`

Explanation:

Your system of equations looks like this

`{(y = 6x-5), (y = -x+9):}`

Notice that `y` is said to be equal to two distinct expressions that depend on `x`, which can only mean that these expressions must be equal to each other.

`6x-5 = -x + 9`

Solve this equation for `x`

`6x + x = 9 + 5`

`7x = 14 implies x= 14/7 = color(green)(2)`

Pick any of the two original equations and find the value of `y`

`y = 6 * (2) - 5`

`y = 12 - 5 = color(green)(7)`

The solution set to this system of equations is

`{(x = 2), (y = 7) :}`