Question

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

Answer 1

`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`