Problem to solve
Solve \[-\frac{3x}{2}+3y+z=2\], \[3x-y+z=5\], \[\frac{x}{3}-y+z=2\]
Solution
STEP 1
Solve the following system:
{-(3 x)/2 + 3 y + z = 2
3 x - y + z = 5
x/3 - y + z = 2
STEP 2
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for z:
{-(3 x)/2 + 3 y + z = 2
3 x - y + z = 5
x/3 - y + z = 2
STEP 3
Hint: | Solve for z.
Subtract 3 y - (3 x)/2 from both sides:
{z = -3 y + (3 x)/2 + 2
3 x - y + z = 5
x/3 - y + z = 2
STEP 4
Hint: | Perform a substitution.
Substitute z = -3 y + (3 x)/2 + 2 into the second and third equations:
{z = -3 y + (3 x)/2 + 2
-4 y + (9 x)/2 + 2 = 5
-4 y + (11 x)/6 + 2 = 2
STEP 5
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for x:
{z = -3 y + (3 x)/2 + 2
-4 y + (9 x)/2 + 2 = 5
-4 y + (11 x)/6 + 2 = 2
STEP 6
Hint: | Isolate terms with x to the left hand side.
Subtract -4 y + 2 from both sides:
{z = -3 y + (3 x)/2 + 2
(9 x)/2 = 4 y + 3
-4 y + (11 x)/6 + 2 = 2
STEP 7
Hint: | Solve for x.
Multiply both sides by 2/9:
{z = -3 y + (3 x)/2 + 2
x = (8 y)/9 + 2/3
-4 y + (11 x)/6 + 2 = 2
STEP 8
Hint: | Perform a substitution.
Substitute x = (8 y)/9 + 2/3 into the third equation:
{z = -3 y + (3 x)/2 + 2
x = (8 y)/9 + 2/3
2 + 11/6 ((8 y)/9 + 2/3) - 4 y = 2
STEP 9
Hint: | Expand the left hand side of the equation 2 + 11/6 ((8 y)/9 + 2/3) - 4 y = 2.
2 + (11 ((8 y)/9 + 2/3))/6 - 4 y = ((44 y)/27 + 11/9) - 4 y + 2 = -(64 y)/27 + 29/9:
{z = -3 y + (3 x)/2 + 2
x = (8 y)/9 + 2/3
(-(64 y)/27 + 29/9) = 2
STEP 10
Hint: | Choose an equation and a variable to solve for.
In the third equation, look to solve for y:
{z = -3 y + (3 x)/2 + 2
x = (8 y)/9 + 2/3
-(64 y)/27 + 29/9 = 2
STEP 11
Hint: | Isolate terms with y to the left hand side.
Subtract 29/9 from both sides:
{z = -3 y + (3 x)/2 + 2
x = (8 y)/9 + 2/3
-(64 y)/27 = -11/9
STEP 12
Hint: | Solve for y.
Multiply both sides by -27/64:
{z = -3 y + (3 x)/2 + 2
x = (8 y)/9 + 2/3
y = 33/64
STEP 13
Hint: | Perform a back substitution.
Substitute y = 33/64 into the first and second equations:
{z = (3 x)/2 + 29/64
x = 9/8
y = 33/64
STEP 14
Hint: | Perform a back substitution.
Substitute x = 9/8 into the first equation:
{z = 137/64
x = 9/8
y = 33/64
STEP 15
Hint: | Sort results.
Collect results in alphabetical order:
Answer: | 
 | {x = 9/8
y = 33/64
z = 137/64