Question

Solve the system of linear equations by substitution. 11x−7y=−14 x−2y=−4

Answer 1

Answer:

x = 1/6 , y = 5/6

Step-by-step explanation:

Solve the following system: using substitution:

{11 x - 7 y = -4

{-14 x - 2 y = -4

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for x:

{11 x - 7 y = -4

{-14 x - 2 y = -4

Hint: | Isolate terms with x to the left hand side.

Add 7 y to both sides:

{11 x = 7 y - 4

{-14 x - 2 y = -4

Hint: | Solve for x.

Divide both sides by 11:

{x = (7 y)/11 - 4/11

{-14 x - 2 y = -4

Hint: | Perform a substitution.

Substitute x = (7 y)/11 - 4/11 into the second equation:

{x = (7 y)/11 - 4/11

{-14 ((7 y)/11 - 4/11) - 2 y = -4

Hint: | Expand the left hand side of the equation -14 ((7 y)/11 - 4/11) - 2 y = -4.

-14 ((7 y)/11 - 4/11) - 2 y = (56/11 - (98 y)/11) - 2 y = 56/11 - (120 y)/11:

{x = (7 y)/11 - 4/11

{56/11 - (120 y)/11 = -4

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for y:

{x = (7 y)/11 - 4/11

{56/11 - (120 y)/11 = -4

Hint: | Isolate terms with y to the left hand side.

Subtract 56/11 from both sides:

{x = (7 y)/11 - 4/11

{-(120 y)/11 = -100/11

Hint: | Solve for y.

Multiply both sides by -11/120:

{x = (7 y)/11 - 4/11

{y = 5/6

Hint: | Perform a back substitution.

Substitute y = 5/6 into the first equation:

Answer:  {x = 1/6 , y = 5/6