How do you solve -2x -8y = 4 and x+ 16y = 22?

Question

1834 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-06T23:29:40

#{(x = -10), (y = 2) :}#

Your system of equations looks like this

#{(-2x - 8y = 4), (x + 16y = 22) :}#

Multiply the second equation by #2# to get

#{(-2x - 8y = 4), (x + 16y = 22 | * (2)) :}#

#{(-2x - 8y = 4), (2x + 32y = 44) :}#

Add these two equations by taking the left-hand sides and the right-hand sides separately

#-color(red)(cancel(color(black)(2x))) - 8y + color(red)(cancel(color(black)(2x))) + 32y = 4 + 44#

#24y = 48 implies y = 48/24 = 2#

Take this value of #y# into one of the original equations and solve for #x#

#x + 16 * (2) = 22#

#x + 32 = 22 implies x = -10#

The solution set for this system will be

#{(x = -10), (y = 2) :}#