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

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