Question

Solve the following system of equations.

x + 3y – z = 2
x – 2y + 3z = 7
x + 2y – 5z = –21

Answer 1

z=16

Answer 2

for which variable

Answer 3

y=119

Answer 4

x=-339

Answer 5

x+3y-z=2
for y :
Move all terms not containing y to the right-hand side of the equation.
3y=-x+z+2

Divide each term in the equation by 3.
(3y)/(3)=-(x)/(3)+(z)/(3)+(2)/(3)

Simplify the left-hand side of the equation by canceling the common terms.
y=-(x)/(3)+(z)/(3)+(2)/(3)

Simplify the right-hand side of the equation by simplifying each term.
y=(-x+z+2)/(3)


for x :
x+3y-z=2

Move all terms not containing x to the right-hand side of the equation.
x=-3y+z+2


for z:
x+3y-z=2

Move all terms not containing z to the right-hand side of the equation.
-z=-x-3y+2

Multiply each term in the equation by -1.
-z*-1=-x*-1-3y*-1+2*-1

Multiply -z by -1 to get z.
z=-x*-1-3y*-1+2*-1

Simplify the right-hand side of the equation by multiplying out all the terms.
z=x+3y-2

Answer 6

x+3y-z=2_x-2y+3z=7_x+2y-5z=-21

Move all terms not containing x to the right-hand side of the equation.
x=-3y+z+2_x-2y+3z=7_x+2y-5z=-21

Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -3y+z+2.
x=-3y+z+2_(-3y+z+2)-2y+3z=7_x+2y-5z=-21

Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -3y+z+2.
x=-3y+z+2_(-3y+z+2)-2y+3z=7_(-3y+z+2)+2y-5z=-21

Remove the parentheses around the expression -3y+z+2.
x=-3y+z+2_-3y+z+2-2y+3z=7_(-3y+z+2)+2y-5z=-21

Since -3y and -2y are like terms, subtract 2y from -3y to get -5y.
x=-3y+z+2_-5y+z+2+3z=7_(-3y+z+2)+2y-5z=-21

Since z and 3z are like terms, add 3z to z to get 4z.
x=-3y+z+2_-5y+4z+2=7_(-3y+z+2)+2y-5z=-21

Remove the parentheses around the expression -3y+z+2.
x=-3y+z+2_-5y+4z+2=7_-3y+z+2+2y-5z=-21

Since -3y and 2y are like terms, subtract 2y from -3y to get -y.
x=-3y+z+2_-5y+4z+2=7_-y+z+2-5z=-21

Since z and -5z are like terms, add -5z to z to get -4z.
x=-3y+z+2_-5y+4z+2=7_-y-4z+2=-21

Move all terms not containing y to the right-hand side of the equation.
x=-3y+z+2_-5y+4z+2=7_-y=4z-2-21

Subtract 21 from -2 to get -23.
x=-3y+z+2_-5y+4z+2=7_-y=4z-23

Multiply each term in the equation by -1.
x=-3y+z+2_-5y+4z+2=7_-y*-1=4z*-1-23*-1

Multiply -y by -1 to get y.
x=-3y+z+2_-5y+4z+2=7_y=4z*-1-23*-1

Simplify the right-hand side of the equation by multiplying out all the terms.
x=-3y+z+2_-5y+4z+2=7_y=-4z+23

Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is -4z+23.
x=-3y+z+2_-5(-4z+23)+4z+2=7_y=-4z+23

Multiply -5 by each term inside the parentheses.
x=-3y+z+2_(20z-115)+4z+2=7_y=-4z+23

Since 20z and 4z are like terms, add 4z to 20z to get 24z.
x=-3y+z+2_24z-115+2=7_y=-4z+23

Add 2 to -115 to get -113.
x=-3y+z+2_24z-113=7_y=-4z+23

Since -113 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 113 to both sides.
x=-3y+z+2_24z=113+7_y=-4z+23

Add 7 to 113 to get 120.
x=-3y+z+2_24z=120_y=-4z+23

Divide each term in the equation by 24.
x=-3y+z+2_(24z)/(24)=(120)/(24)_y=-4z+23

Simplify the left-hand side of the equation by canceling the common terms.
x=-3y+z+2_z=(120)/(24)_y=-4z+23

Simplify the right-hand side of the equation by simplifying each term.
x=-3y+z+2_z=5_y=-4z+23

Replace all occurrences of z with the solution found by solving the last equation for z. In this case, the value substituted is 5.
x=-3y+(5)+2_z=5_y=-4z+23

Replace all occurrences of z with the solution found by solving the last equation for z. In this case, the value substituted is 5.
x=-3y+(5)+2_z=5_y=-4(5)+23

Remove the parentheses around the expression 5.
x=-3y+5+2_z=5_y=-4(5)+23

Add 2 to 5 to get 7.
x=-3y+7_z=5_y=-4(5)+23

Multiply -4 by each term inside the parentheses.
x=-3y+7_z=5_y=-20+23

Add 23 to -20 to get 3.
x=-3y+7_z=5_y=3

Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 3.
x=-3(3)+7_z=5_y=3

Multiply -3 by each term inside the parentheses.
x=-9+7_z=5_y=3

Add 7 to -9 to get -2.
x=-2_z=5_y=3

This is the solution to the system of equations.
x=-2_z=5_y=3