Question

Solve the system using substitution or elimination:

8x - 3y = -13
-3x + 5y = 1
Make sure you answer is an ordered pair (x, y).

Answer 1

{x = -2, y = -1

Explanation:

Solve the following system:

{-3 y + 8 x = -13

5 y - 3 x = 1

Choose an equation and a variable to solve for.

In the first equation, look to solve for x:

{-3 y + 8 x = -13

5 y - 3 x = 1

Isolate terms with x to the left-hand side.

Add 3 y to both sides:

{8 x = 3 y - 13

5 y - 3 x = 1

Hint: | Solve for x.

Divide both sides by 8:

{x = (3 y)/8 - 13/8

5 y - 3 x = 1

Perform a substitution.

Substitute x = (3 y)/8 - 13/8 into the second equation:

{x = (3 y)/8 - 13/8

5 y - 3 ((3 y)/8 - 13/8) = 1

Expand the left-hand side of the equation 5 y - 3 ((3 y)/8 - 13/8) = 1.

5 y - 3 ((3 y)/8 - 13/8) = 5 y + (-(9 y)/8 + 39/8) = (31 y)/8 + 39/8:

{x = (3 y)/8 - 13/8

((31 y)/8 + 39/8) = 1

Choose an equation and a variable to solve for.

In the second equation, look to solve for y:

{x = (3 y)/8 - 13/8

(31 y)/8 + 39/8 = 1

Isolate terms with y to the left-hand side.

Subtract 39/8 from both sides:

{x = (3 y)/8 - 13/8

(31 y)/8 = -31/8

Solve for y.

Multiply both sides by 8/31:

{x = (3 y)/8 - 13/8

y = -1

Hint: | Perform a back substitution.

Substitute y = -1 into the first equation:

Answer: {x = -2, y = -1