Question

How do you solve the system of equations `x+ 3y = - 14` and `2x - 4y = 30`?

Answer 1

`(x,y)to(17/5,-29/5)`

Explanation:

`x+3y=-14to(1)`

`2x-4y=30to(2)`

`"rearrange equation "(1)" expressing x in terms of y"`

`x=-14-3yto(3)`

`"substitute "x=-14-3y" into equation "(2)`

`2(-14-3y)-4y=30larrcolor(blue)"distribute"`

`-28-6y-4y=30larrcolor(blue)"simplify"`

`-28-10y=30`

`"add 28 to both sides"`

`-10y=58`

`"divide both sides by "-10`

`y=58/(-10)=-29/5`

`"substitute this value into equation "(3)" for x"`

`x=-14-(3xx-29/5)=-70/5+87/5=17/5`

`"solution is "(x,y)to(17/5,-29/5)`