Problem to solve
Solve \[3x+5y=2\], \[-5x+6y=5\]
Solution
STEP 1
Solve the following system:
{5 y + 3 x = 2
6 y - 5 x = 5
STEP 2
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for x:
{5 y + 3 x = 2
6 y - 5 x = 5
STEP 3
Hint: | Isolate terms with x to the left hand side.
Subtract 5 y from both sides:
{3 x = -5 y + 2
6 y - 5 x = 5
STEP 4
Hint: | Solve for x.
Divide both sides by 3:
{x = -(5 y)/3 + 2/3
6 y - 5 x = 5
STEP 5
Hint: | Perform a substitution.
Substitute x = -(5 y)/3 + 2/3 into the second equation:
{x = -(5 y)/3 + 2/3
6 y - 5 (-(5 y)/3 + 2/3) = 5
STEP 6
Hint: | Expand the left hand side of the equation 6 y - 5 (-(5 y)/3 + 2/3) = 5.
6 y - 5 (-(5 y)/3 + 2/3) = ((25 y)/3 - 10/3) + 6 y = (43 y)/3 - 10/3:
{x = -(5 y)/3 + 2/3
((43 y)/3 - 10/3) = 5
STEP 7
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for y:
{x = -(5 y)/3 + 2/3
(43 y)/3 - 10/3 = 5
STEP 8
Hint: | Isolate terms with y to the left hand side.
Add 10/3 to both sides:
{x = -(5 y)/3 + 2/3
(43 y)/3 = 25/3
STEP 9
Hint: | Solve for y.
Multiply both sides by 3/43:
{x = -(5 y)/3 + 2/3
y = 25/43
STEP 10
Hint: | Perform a back substitution.
Substitute y = 25/43 into the first equation:
Answer: | 
 | {x = -13/43
y = 25/43