How do you solve x + y = 23 and y = x - 5?

2 Answers
Feb 15, 2016

x=14 and y=9

Explanation:

Since y=x-5 in the second equation, we may substitute this fact into the first equation and then solve for x.
Doing so we get :

x+(x-5)=23

therefore 2x=28

therefore x=14.

Now back-substitute to get y=14-5=9.

Feb 15, 2016

The solution for the system of equations is:
color(blue)(x=14

color(blue)(y=9

Explanation:

x+y=23.......equation 1
x-y=5..........equation 2

Solving by elimination.

Adding equations 1 and 2

x+cancelcolor(blue)(y)=23
x-cancelcolor(blue)(y)=5

2x=28

x=28/2

color(blue)(x=14

Finding y from equation 1:
x+y=23

y=23-x

y=23-14

color(blue)(y=9