Question

Solve the following equations for the ordered pair. -x-6y =20 and -2x +5y=6

Answer 1

Answer: (–8, –2)

Step-by-step explanation

Given

`-x-6y=20`
`-2x+5y=6`

To solve the equations we need to isolate one variable in one equation, substitute the obtained expression in the second equation, and then obtain the variable's value. Finally, we replace this value in the first variable's isolated expression and get the result.

0. Isolate one variable in one equation

`-x-6y+6y=20+6y`
`-x=20+6y`
`-x\cdot-1=(20+6y)\cdot-1`
`x=-20-6y`

2. Now, we have to substitute the obtained expression in the second equation

`-2(-20-6y)+5y=6`
`40+12y+5y=6`

3. Next, we can obtain the value of the variable by solving for y:

`40+17y=6`
`40-40+17y=6-40`
`17y=-34`
`(17y)/(17)=(-34)/(17)`
`y=-2`

4. We replace this value in the x isolated expression:

`x=-20-6(-2)`
`x=-20+12`
`x=-8`

3. Finally, we write the result in an ordered pair (x, y): (–8, –2)