Question

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

Answer 1

`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:

`2x+8y=32`

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

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

and, by symplifying, you have:

`5y=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):

`-8x-12y=-68 and 3x+12y=48`

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

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

and, by symplifying:

`-5x=-20`

by which:

`x=4`