Question

How do you solve the system of equations `-2x-8y=10` and `2x-6y=18` by elimination?

Answer 1

The solution is : `(x=+2; y=-2)`
Shown below ...

Explanation:

You have two equations and two unknowns. Using one equation you can write one variable in terms of the other, thereby eliminating one variable. Then solve for the existing variable. Once that is solved the eliminated variable can be evaluated.

`-2x-8y=10` ...... (1)
`2x-6y=18` .......... (2)

Equation (1) can be written as : `2x = -(8y + 10)`,

Substitute this in equation 2: `-(8y + 10)-6y = 18`

We have eliminated `x` and have an equation with only `y`

Rearranging, `-14y = 28; \qquad => y = -2`

Put this back in either of the two equations (1 or 2),

Equation 2 : `2x = 18 + 6y = 18 + 6\times(-2) = 6`

Therefore `x=+2`.

Answer 2

`x,y=3,-2`

Explanation:

`color(blue)(-2x-8y=10),color(red)(2x-6y=18)`

We can eiminate -2x frpm the firt expreesssion by 2x in the second equatrion

So Add the equations

`rarr(-2x-8y=10)+(2x-6y=18)`

`rarr-14y=28`

`rArrcolor(green)(y=-28/14=-2`

So,Substitute the value of y to the second equatipn

`rarr-2x-8(-2)=10`

`rarr-2x-(-16)=10`

`rarr-2x+16=10`

`rarr-2x=10-16`

`rarr-2x=-6`

`rArrcolor(green)(x=(-6)/-2=6/2=3`