Answer:
x = -7
, y = -9
Step-by-step explanation:
Solve the following system:
{8 y - 9 x = -9
8 y - 10 x = -2
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for x:
{8 y - 9 x = -9
8 y - 10 x = -2
Hint: | Isolate terms with x to the left hand side.
Subtract 8 y from both sides:
{-9 x = -8 y - 9
8 y - 10 x = -2
Hint: | Solve for x.
Divide both sides by -9:
{x = (8 y)/9 + 1
8 y - 10 x = -2
Hint: | Perform a substitution.
Substitute x = (8 y)/9 + 1 into the second equation:
{x = (8 y)/9 + 1
8 y - 10 ((8 y)/9 + 1) = -2
Hint: | Expand the left hand side of the equation 8 y - 10 ((8 y)/9 + 1) = -2.
8 y - 10 ((8 y)/9 + 1) = 8 y + (-(80 y)/9 - 10) = -(8 y)/9 - 10:
{x = (8 y)/9 + 1
-(8 y)/9 - 10 = -2
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for y:
{x = (8 y)/9 + 1
-(8 y)/9 - 10 = -2
Hint: | Isolate terms with y to the left hand side.
Add 10 to both sides:
{x = (8 y)/9 + 1
-(8 y)/9 = 8
Hint: | Solve for y.
Multiply both sides by -9/8:
{x = (8 y)/9 + 1
y = -9
Hint: | Perform a back substitution.
Substitute y = -9 into the first equation:
Answer: {x = -7
, y = -9
