Question

How do you solve the system of equations `y= x + 2` and `y = 5x + 5`?

Answer 1

`(-3/4,5/4)`

Explanation:

Since both equations are expressed in terms of y we can equate the right sides.

`rArr5x+5=x+2larr" solve for x"`

subtract x from both sides.

`5x-x+5=cancel(x)cancel(-x)+2`

`rArr4x+5=2`

subtract 5 from both sides.

`4xcancel(+5)cancel(-5)=2-5`

`rArr4x=-3`

divide both sides by 4

`(cancel(4) x)/cancel(4)=(-3)/4`

`rArrx=-3/4`

Substitute this value into either of the 2 equations to obtain y

`"Using "y=x+2`

`x=-3/4toy=-3/4+2=5/4`

`"the solution is "(-3/4,5/4)`
graph{(y-x-2)(y-5x-5)=0 [-10, 10, -5, 5]}