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

1 Answer
Jun 18, 2016

Answer:

#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#