Problem to solve
Solve \[\frac{3}{2}x-\frac{1}{2}y=6x-2\], \[3x+\frac{2}{3}y=-2y-1\]
Solution
STEP 1
Solve the following system:
{-y/2 + (3 x)/2 = 6 x - 2
(2 y)/3 + 3 x = -2 y - 1
STEP 2
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for y:
{-y/2 + (3 x)/2 = 6 x - 2
(2 y)/3 + 3 x = -2 y - 1
STEP 3
Hint: | Isolate terms with y to the left hand side.
Subtract (3 x)/2 from both sides:
{-y/2 = 1/2 (9 x - 4)
(2 y)/3 + 3 x = -2 y - 1
STEP 4
Hint: | Solve for y.
Multiply both sides by -2:
{y = -9 x + 4
(2 y)/3 + 3 x = -2 y - 1
STEP 5
Hint: | Perform a substitution.
Substitute y = -9 x + 4 into the second equation:
{y = -9 x + 4
2/3 (-9 x + 4) + 3 x = -2 (-9 x + 4) - 1
STEP 6
Hint: | Expand the left hand side of the equation 2/3 (-9 x + 4) + 3 x = -2 (-9 x + 4) - 1.
(2 (-9 x + 4))/3 + 3 x = 3 x + (-6 x + 8/3) = -3 x + 8/3:
{y = -9 x + 4
(-3 x + 8/3) = -2 (-9 x + 4) - 1
STEP 7
Hint: | Expand the right hand side of the equation -3 x + 8/3 = -2 (-9 x + 4) - 1.
-2 (-9 x + 4) - 1 = (18 x - 8) - 1 = 18 x - 9:
{y = -9 x + 4
-3 x + 8/3 = (18 x - 9)
STEP 8
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for x:
{y = -9 x + 4
-3 x + 8/3 = 18 x - 9
STEP 9
Hint: | Isolate x to the left hand side.
Subtract 18 x + 8/3 from both sides:
{y = -9 x + 4
-21 x = -35/3
STEP 10
Hint: | Solve for x.
Divide both sides by -21:
{y = -9 x + 4
x = 5/9
STEP 11
Hint: | Perform a back substitution.
Substitute x = 5/9 into the first equation:
{y = -1
x = 5/9
STEP 12
Hint: | Sort results.
Collect results in alphabetical order:
Answer: | 
 | {x = 5/9
y = -1