Question

How do you solve the system of equations `-16x - 4y = 12` and `- 4x + y = - 11`?

Answer 1

`x=1 and y=-7`

Explanation:

Given 2 equations, let us number them

`-16x-4y=12`
we can simplify this equation by 4 , it would be easier for solving

`rArr(-16x-4y)/4=12/4`
`rArrcolor(blue)(-4x-y=3` equation1

the two equations are:

`color(blue)(-4x-y=3)`
`color(red)(-4x+y=-11)`

First we add both equations :
`color(blue)(-4x-y)color(red)(-4x+y)=3-11`
`-8x+0y=-8`
`-8x=-8`
`x=-8/-8`
`color(green)(x=1)`

second, let us substitute the value of `x` in equation 2
`color(red)(-4*1+y=-11)`
`rArr-4+y=-11`
`rArry=-11+4`
`color(green)(y=-7)`

Third, check if the values `color(green)(x=1 and color(green)(y=-7)` by substituting it in equation 1
`color(blue)(-4x-y=3)`
`color(blue)(-4(color(green)1)-(color(green)(-7))=?3)`
`color(blue)(-4+7=?3)`
`-3=?-3 true`

therefore,x=1 and y=-7#