How do you solve the system of equations $2 x + 2 y = 130$ $2x + 2y = 130$ and $x - y = 35$ $x - y = 35$ ?

Question

1523 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-08T20:08:30

$x = 50$ $x=50$

$y = 15$ $y=15$

Using the second equation, solve for $x$ $x$ by adding $y$ $y$ to both sides:
$x = 35 + y$ $x=35+y$

Substitute this quantity in for $x$ $x$ in the first equation:
$2 (35 + y) + 2 y = 130$ $2(35+y)+2y=130$

Distribute:
$70 + 2 y + 2 y = 130$ $70+2y+2y=130$

Simplify by adding like terms:
$70 + 4 y = 130$ $70+4y=130$

Subtract $70$ $70$ from both sides:
$4 y = 60$ $4y=60$

Divide each side by $4$ $4$
$y = 15$ $y=15$

Substitute $15$ $15$ in for $y$ $y$ in second equation:
$x - (15) = 35$ $x-(15)=35$

Add $15$ $15$ to both sides:
$x = 50$ $x=50$

How do you solve the system of equations 2x + 2y = 1302x+2y=1302x + 2y = 130 and x - y = 35x−y=35x - y = 35?