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

1 Answer
Apr 26, 2018

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