Answer:
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
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