How do you find the solution of the system of equations #x-4y=6# and #3x+4y=10#?

1 Answer
Apr 26, 2018

Answer:

#x=4#
#y=-0.5#

Explanation:

Because that we have one single x in one of the terms, I'm going to use the substitution method.

Given that:

#x-4y=6#
#3x+4y=10#

We can rewrite the first term to get what x equals to:

#x-4y=6 => color(green)(x=6+4y)#

Now put that in the other system to get:

#3x+4y=10=> 3 (color(green)(6+4y))+4y = 10#

And now simplify and collect terms:

#(3xx6)+(3xx4y)+4y=10#

#18+12y+4y=10#

#18+16y=10#

#16y=-8#

Now divide 16 on both sides to get y:

#(16y)/color(blue)16=-8/color(blue)16#

#y=-0.5#

Now put that into one of the two systems to get x.

#x-4y=6=> x-4 color(green)((-0.5))=6#

#x color(green)(+2)=6#

#x=4#

Now check your work:

#3x+4y=10=>3 color(green)((4))+4 color(green)((-0.5))=10#

#12-2=10# #color(green)sqrt#