Problem to solve
Solve \[\frac{2x}{3}-2z=-2\], \[2y-4z=2\], \[\frac{x}{3}-5y=2\]
Solution
STEP 1
Solve the following system:
{-2 z + (2 x)/3 = -2
-4 z + 2 y = 2
-5 y + x/3 = 2
STEP 2
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for x:
{-2 z + (2 x)/3 = -2
-4 z + 2 y = 2
-5 y + x/3 = 2
STEP 3
Hint: | Isolate terms with x to the left hand side.
Add 2 z to both sides:
{(2 x)/3 = 2 z - 2
-4 z + 2 y = 2
-5 y + x/3 = 2
STEP 4
Hint: | Solve for x.
Multiply both sides by 3/2:
{x = 3 z - 3
-4 z + 2 y = 2
-5 y + x/3 = 2
STEP 5
Hint: | Perform a substitution.
Substitute x = 3 z - 3 into the third equation:
{x = 3 z - 3
-4 z + 2 y = 2
1/3 (3 z - 3) - 5 y = 2
STEP 6
Hint: | Expand the left hand side of the equation 1/3 (3 z - 3) - 5 y = 2.
(3 z - 3)/3 - 5 y = (z - 1) - 5 y = z - 5 y - 1:
{x = 3 z - 3
-4 z + 2 y = 2
(z - 5 y - 1) = 2
STEP 7
Hint: | Choose an equation and a variable to solve for.
In the third equation, look to solve for z:
{x = 3 z - 3
-4 z + 2 y = 2
z - 5 y - 1 = 2
STEP 8
Hint: | Solve for z.
Add 5 y + 1 to both sides:
{x = 3 z - 3
-4 z + 2 y = 2
z = 5 y + 3
STEP 9
Hint: | Perform a substitution.
Substitute z = 5 y + 3 into the second equation:
{x = 3 z - 3
2 y - 4 (5 y + 3) = 2
z = 5 y + 3
STEP 10
Hint: | Expand the left hand side of the equation 2 y - 4 (5 y + 3) = 2.
2 y - 4 (5 y + 3) = 2 y + (-20 y - 12) = -18 y - 12:
{x = 3 z - 3
(-18 y - 12) = 2
z = 5 y + 3
STEP 11
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for y:
{x = 3 z - 3
-18 y - 12 = 2
z = 5 y + 3
STEP 12
Hint: | Isolate terms with y to the left hand side.
Add 12 to both sides:
{x = 3 z - 3
-18 y = 14
z = 5 y + 3
STEP 13
Hint: | Solve for y.
Divide both sides by -18:
{x = 3 z - 3
y = -7/9
z = 5 y + 3
STEP 14
Hint: | Perform a back substitution.
Substitute y = -7/9 into the third equation:
{x = 3 z - 3
y = -7/9
z = -8/9
STEP 15
Hint: | Perform a back substitution.
Substitute z = -8/9 into the first equation:
Answer: | 
 | {x = -17/3
y = -7/9
z = -8/9