Question

What is the solution of the system `y=x-10, y=2x+5`?

Answer 1

`x = -15 and y = -25`

Explanation:

This is a perfect scenario for solving the two equations.
(which represent straight lines and the solution gives the point of intersection.)

`color(blue)(y = x-10)" and "color(red)(y = 2x+5)`

The two `y-` values are equal!

`color(white)(xxxxxxxxxxxxx)color(blue)(y) = color(red)(y)`

Therefore:`color(white)(xxx)color(blue)(x-10) =color(red)(2x+5)`

`color(white)(xxxx.xxx)-10-5 =2x-x`

`color(white)(xxxx.xxx)-15 =x" "larr` we have the x-value

`y = (-15)-10 = -25" "larr` from the first equation

Check in the second equation:

`y = 2(-15)+5 = -25`

`x = -15 and y = -25`