Question

I DONT KNOW HOW TO SOLVE SYSTEMS BY SUBSTITUTION
PLEASE HELP

Answer 1

Solve the second equation for x ( x = -13 - 3y) and then substitute the value into first equation

Solve the first equation for y( y = 2x - 9 ) and then substitute that value into second equation

solve either equation for 3y ( 3y = -13 - x or 3y = 6x - 27) and then substitute that value into other equation

Solution:

Given system of equations are:

6x - 3y = 27 ------- eqn 1

x + 3y = -13 -------- eqn 2

We have to solve the above system of equations by substitution method

Solve the second equation for x ( x = -13 - 3y) and then substitute the value into first equation

Solve the eqn 2 for variable "x"

From eqn 2,

x + 3y = -13

x = -3y - 13 ------- eqn 3

Substitute eqn 3 in eqn 1

6(-3y - 13) - 3y = 27

-18y - 78 - 3y = 27

Combine the like terms

-18y - 3y - 78 = 27

-21y = 27 + 78

-21y = 105

`y = (-105)/(21)= -5`

y = -5

Substitute y =-5 in eqn 2

x + 3(-5) = -13

x - 15 = -13

x = -13 + 15

x = 2

Thus the solution is (x, y) = (2, -5)