Question

How do you solve the following system: `6x+2y=-4, -x+y=5`?

Answer 1

`6*x+2*y=-4`
`-x+y=5`
multiply 2nd by 2, gives.
`-2*x+2*y=10`
subtract from top.
`8*x=-14`
`x= -14/8=-1.75`
`1.75+y=5`
`y=5-1.75=3.25`
check `6*-1.75+2*3.25=-4`

Answer 2

`(x,y)=(-7/4,13/4)`

Explanation:

Solve by elimination and substitution

`color(blue)(6x+2y=-4`

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

Multiply the second equation by `-2`

`rarr-2(-x+y=5)`

`rarr2x-2y=-10`

Now,eliminate `2y` in the first equation by `-2y` in the second equation

Add both the equations

`rarr(6x+2y=-4)+(2x-2y=-10)`

`rarr8x=-14`

`color(green)(rArrx=-14/8=-7/4`

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

`rarr-(-7/4)+y=5`

`rarr7/4+y=5`

`color(green)(rArry=5-7/4=13/4`