Question

How do you solve the following system: `6x + y = 2, 5x + 8y = -2`?

Answer 1

`(x,y)=(-22/43,18/43)`

Explanation:

Solve by elimination substitution

`color(blue)(6x+y=2`

`color(blue)(5x+8y=-2`

We can eliminate `8y` in the second equation by `y` in the first equation if we multiply (whole equation) `y` with `-8` to get `-8y`

`rarr-8(6x+y=2)`

Use distributive property

`color(brown)(a(b+c=x)=ab+ac=ax`

`rarr-48x-8y=-16`

Now,add the above equation to the second equation to eliminate `8y`

`rarr(-48x-8y=-16)+(5x+8y=-2)`

`rarr-43x=-18`

Divide both sides by `-43`

`rarr(cancel(-43)x)/cancel(-43)=(-18)/-43`

`color(green)(rArrx=18/43`

Because,

`color(brown)((-a)/-b=a/b`

Now,substitute the value of `x` to the first equation

`rarr6(18/43)+y=2`

`rarr108/43+y=2`

`rarr(108+43y)/43=2`

Multiply both sides by `43`

`rarr(108+43y)/cancel43*cancel43=2*43`

`rarr108+43y=86`

Subtract `108` both sides

`rarr108+43y-108=86-108`

`rarr43y=-22`

Divide both sides by `43`

`rarr(cancel43y)/cancel43=-22/43`

`color(green)(rArry=-22/43`

`color(blue)(ul bar |(x,y)=(-22/43,18/43)|`