Problem to solve
Solve \[\frac{6}{5}x+\frac{3}{2}y=5\], \[-\frac{3}{5}x+y=5y+2\]
Solution
STEP 1
Solve the following system:
{(3 y)/2 + (6 x)/5 = 5
y - (3 x)/5 = 5 y + 2
STEP 2
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for x:
{(3 y)/2 + (6 x)/5 = 5
y - (3 x)/5 = 5 y + 2
STEP 3
Hint: | Isolate terms with x to the left hand side.
Subtract (3 y)/2 from both sides:
{(6 x)/5 = 1/2 (-3 y + 10)
y - (3 x)/5 = 5 y + 2
STEP 4
Hint: | Solve for x.
Multiply both sides by 5/6:
{x = 5/12 (-3 y + 10)
y - (3 x)/5 = 5 y + 2
STEP 5
Hint: | Perform a substitution.
Substitute x = 5/12 (-3 y + 10) into the second equation:
{x = 5/12 (-3 y + 10)
y + 1/4 (3 y - 10) = 5 y + 2
STEP 6
Hint: | Expand the left hand side of the equation y + 1/4 (3 y - 10) = 5 y + 2.
y + (3 y - 10)/4 = y + ((3 y)/4 - 5/2) = (7 y)/4 - 5/2:
{x = 5/12 (-3 y + 10)
((7 y)/4 - 5/2) = 5 y + 2
STEP 7
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for y:
{x = 5/12 (-3 y + 10)
(7 y)/4 - 5/2 = 5 y + 2
STEP 8
Hint: | Isolate y to the left hand side.
Subtract 5 y - 5/2 from both sides:
{x = 5/12 (-3 y + 10)
-(13 y)/4 = 9/2
STEP 9
Hint: | Solve for y.
Multiply both sides by -4/13:
{x = 5/12 (-3 y + 10)
y = -18/13
STEP 10
Hint: | Perform a back substitution.
Substitute y = -18/13 into the first equation:
Answer: | 
 | {x = 230/39
y = -18/13