Question 217068: Can someone help me solve the systems of equations?
3x+4y+z=7
2y+z=3
-5xz+3y+8z=-31
Answer by DRichardson(63)   (Show Source):
You can put this solution on YOUR website! Hello There,
Equation 3*x+4*y+z=7
Simplifying
3x + 4y + z = 7
Solving
3x + 4y + z = 7
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4y' to each side of the equation.
3x + 4y + -4y + z = 7 + -4y
Combine like terms: 4y + -4y = 0
3x + 0 + z = 7 + -4y
3x + z = 7 + -4y
Add '-1z' to each side of the equation.
3x + z + -1z = 7 + -4y + -1z
Combine like terms: z + -1z = 0
3x + 0 = 7 + -4y + -1z
3x = 7 + -4y + -1z
Divide each side by '3'.
x = 2.333333333 + -1.333333333y + -0.3333333333z
Simplifying
x = 2.333333333 + -1.333333333y + -0.3333333333z
Simplifying
2y + z = 3
Solving
2y + z = 3
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-1z' to each side of the equation.
2y + z + -1z = 3 + -1z
Combine like terms: z + -1z = 0
2y + 0 = 3 + -1z
2y = 3 + -1z
Divide each side by '2'.
y = 1.5 + -0.5z
Simplifying
y = 1.5 + -0.5z
Simplifying
-5xz + 3y + 8z = -31
Solving
-5xz + 3y + 8z = -31
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3y' to each side of the equation.
-5xz + 3y + -3y + 8z = -31 + -3y
Combine like terms: 3y + -3y = 0
-5xz + 0 + 8z = -31 + -3y
-5xz + 8z = -31 + -3y
Add '-8z' to each side of the equation.
-5xz + 8z + -8z = -31 + -3y + -8z
Combine like terms: 8z + -8z = 0
-5xz + 0 = -31 + -3y + -8z
-5xz = -31 + -3y + -8z
Divide each side by '-5z'.
x = 6.2z-1 + 0.6yz-1 + 1.6
Simplifying
x = 6.2z-1 + 0.6yz-1 + 1.6
Reorder the terms:
x = 1.6 + 0.6yz-1 + 6.2z-1
Hope this helps! And is not too complicated!
Delilah R.
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