Question

How do you solve the system of equations `8x + 7y = - 6` and `14x + 14y = 13`?

Answer 1

`color(green)(x = -12 (1/2) , " "y = -15(1/7)`

Explanation:

`8x + 7y = -6`

`16x + 14y = -12, " Multiplying by 2 on both sides" color(red)(" Eqn 1"`

`14x + 14 y = 13, color(red)(" Eqn 2"`

Subtract Eqn 2 from Eqn 1,

`16x - 14 x +cancel( 14y) - cancel(14y) = -12 - 13`

`2x = -25 " or " x = -25/2`

Substituting the value of x in Eqn 1,

`(16 * (25/2)) + 14 y = -12`

`200 + 14 y = -12`

`14y = -12 -200 = -214`

`y = -212 / 14 = -106 / 7 = -15(1/7)`