Answer:
{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