Systems of equations in two variables with applications

-2x+7y=2

3x-5y=-14

Onne way is to eliminate terms

-2x+7y=2

3x-5y=-14

multiply first equation by 3 and second equaiton by 2

-6x+21y=6

6x-10y=-28

add them together to cancel x terms

-6x+21y=6

6x-10y=-28 +

0x+11y=-22

11y=-22

divide by 11

y=-2

subsitute

-2x+7 (-2) = 2

-2x-14=2

add 14 to both sides

-2x=16

divide both sides by 2

-x=8

multiply - 1

x=-8

x=-8

y=-2

in (x, y) form

(-8,-2)