Question

How do you solve this linear equation by substitution x+7y=-5 2x-3y=5

Answer 1

Substitution method can be applied in four steps

Step 1: Solve one of the equations for either x = or y = .

Step 2: Substitute the solution from step 1 into the other equation.

Step 3: Solve this new equation.

Step 4: Solve for the second variable.

Given linear equations

x + 7y = -5 , 2x - 3y = 5

Step 1: Solve one of the equations for either x = or y =

x + 7y = -5

x = -5 - 7y

Step 2: Substitute the solution from step 1 into the second equation.

2x -3y =5

2(-5 - 7y) - 3y = 5

Step 3: Solve this new equation.

2(-5 - 7y) - 3y = 5

-10 -14y - 3y = 5

-10 - 17y = 5

-17y = 5 + 10

-17y = 15

y = -15 / 17

Step 4: Solve for the second variable

For x = -5 -7y

x = -5 -7(-15/17)

x = -5 - (-105/17)

x =( -5(17) + 105 ) / 17

x= (-85 + 105 ) / 17

x = 20 /17

Therefore x = 20 / 17 , y = -15 / 17