Problem to solve
Solve \[-x+3y+2z=5\], \[-3x-2y+z=-4\], \[x-y+z=3\]
Solution
STEP 1
Solve the following system:
{-x + 3 y + 2 z = 5
-3 x - 2 y + z = -4
x - y + z = 3
STEP 2
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for z:
{-x + 3 y + 2 z = 5
-3 x - 2 y + z = -4
x - y + z = 3
STEP 3
Hint: | Solve for z.
Add 2 y + 3 x to both sides:
{-x + 3 y + 2 z = 5
z = 2 y + 3 x - 4
x - y + z = 3
STEP 4
Hint: | Perform a substitution.
Substitute z = 2 y + 3 x - 4 into the first and third equations:
{-x + 3 y + 2 (2 y + 3 x - 4) = 5
z = 2 y + 3 x - 4
y + 4 x - 4 = 3
STEP 5
Hint: | Expand the left hand side of the equation -x + 3 y + 2 (2 y + 3 x - 4) = 5.
-x + 3 y + 2 (2 y + 3 x - 4) = -x + 3 y + (4 y + 6 x - 8) = 7 y + 5 x - 8:
{(7 y + 5 x - 8) = 5
z = 2 y + 3 x - 4
y + 4 x - 4 = 3
STEP 6
Hint: | Choose an equation and a variable to solve for.
In the third equation, look to solve for y:
{7 y + 5 x - 8 = 5
z = 2 y + 3 x - 4
y + 4 x - 4 = 3
STEP 7
Hint: | Solve for y.
Subtract 4 x - 4 from both sides:
{7 y + 5 x - 8 = 5
z = 2 y + 3 x - 4
y = -4 x + 7
STEP 8
Hint: | Perform a substitution.
Substitute y = -4 x + 7 into the first equation:
{-8 + 7 (-4 x + 7) + 5 x = 5
z = 2 y + 3 x - 4
y = -4 x + 7
STEP 9
Hint: | Expand the left hand side of the equation -8 + 7 (-4 x + 7) + 5 x = 5.
-8 + 7 (-4 x + 7) + 5 x = 5 x + (-28 x + 49) - 8 = -23 x + 41:
{(-23 x + 41) = 5
z = 2 y + 3 x - 4
y = -4 x + 7
STEP 10
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for x:
{-23 x + 41 = 5
z = 2 y + 3 x - 4
y = -4 x + 7
STEP 11
Hint: | Isolate terms with x to the left hand side.
Subtract 41 from both sides:
{-23 x = -36
z = 2 y + 3 x - 4
y = -4 x + 7
STEP 12
Hint: | Solve for x.
Divide both sides by -23:
{x = 36/23
z = 2 y + 3 x - 4
y = -4 x + 7
STEP 13
Hint: | Perform a back substitution.
Substitute x = 36/23 into the second and third equations:
{x = 36/23
z = 2 y + 16/23
y = 17/23
STEP 14
Hint: | Perform a back substitution.
Substitute y = 17/23 into the second equation:
{x = 36/23
z = 50/23
y = 17/23
STEP 15
Hint: | Sort results.
Collect results in alphabetical order:
Answer: | 
 | {x = 36/23
y = 17/23
z = 50/23