# How do you solve the system by addition –2x – 3y = –17 and x + 4y = 16?

Jun 18, 2016

$x = 4$ and $y = 3$

#### Explanation:

first, you must have opposite terms in x or in y, in this case to join this for x you simply must multiply all terms of the second equation by 2 to have:

$2 x + 8 y = 32$

now you can sum the terms of the equations to have:

$- 2 x - 3 y + 2 x + 8 y = - 17 + 32$

and, by symplifying, you have:

$5 y = 15$

by which:

$y = 3$

You can go on by substitution to have x, but if you again use addition, you can multiply the terms of the first equation by 4 and the terms of the second equation by 3, to have opposite terms in both equations (-12y and +12y):

$- 8 x - 12 y = - 68 \mathmr{and} 3 x + 12 y = 48$

Then, by adding all terms of the first one to all terms of the second one:

$- 8 x + 3 x - 12 y + 12 y = - 68 + 48$

and, by symplifying:

$- 5 x = - 20$

by which:

$x = 4$