Answer:
x = 9 , y = 12
Step-by-step explanation:
Solve the following system:
{4 y - 5 x = 3
x = 2 y - 15
Hint: | Perform a substitution.
Substitute x = 2 y - 15 into the first equation:
{4 y - 5 (2 y - 15) = 3
x = 2 y - 15
Hint: | Expand the left-hand side of the equation 4 y - 5 (2 y - 15) = 3.
4 y - 5 (2 y - 15) = 4 y + (75 - 10 y) = 75 - 6 y:
{75 - 6 y = 3
x = 2 y - 15
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for y:
{75 - 6 y = 3
x = 2 y - 15
Hint: | Isolate terms with y to the left-hand side.
Subtract 75 from both sides:
{-6 y = -72
x = 2 y - 15
Hint: | Solve for y.
Divide both sides by -6:
{y = 12
x = 2 y - 15
Hint: | Perform a back substitution.
Substitute y = 12 into the second equation:
{y = 12
x = 9
Hint: | Sort results.
Collect results in alphabetical order:
Answer: {x = 9 , y = 12
