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

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Answer 1 · 2016-02-15T18:05:46

$x = 14 and y = 9$ $x=14 and y=9$

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

$x + (x - 5) = 23$ $x+(x-5)=23$

$therefore 2x=28$

$therefore x=14$ .

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

Answer 2 · 2016-02-15T18:08:37

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

$color(blue)(y=9$

$x+y=23$ .......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 $1$ :
$x+y=23$

$y=23-x$

$y=23-14$

$color(blue)(y=9$