SOLUTION: 5x+3y+z=14 x-3y+2z=-8 14x-2y+3z=-22

Question 350722: 5x+3y+z=14
x-3y+2z=-8
14x-2y+3z=-22
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
Are all of these a set of liear equations or seperate?
If they are all together, then you would use the substitution method:
5x+3y+z=14_x-3y+2z=-8_14x-2y+3z=-22
Move all terms not containing z to the right-hand side of the equation.
z=-5x-3y+14_x-3y+2z=-8_14x-2y+3z=-22
Replace all occurrences of z with the solution found by solving the last equation for z. In this case, the value substituted is -5x-3y+14.
z=-5x-3y+14_x-3y+2(-5x-3y+14)=-8_14x-2y+3z=-22
Replace all occurrences of z with the solution found by solving the last equation for z. In this case, the value substituted is -5x-3y+14.
z=-5x-3y+14_x-3y+2(-5x-3y+14)=-8_14x-2y+3(-5x-3y+14)=-22
Multiply 2 by each term inside the parentheses.
z=-5x-3y+14_x-3y-10x-6y+28=-8_14x-2y+3(-5x-3y+14)=-22
Since x and -10x are like terms, add -10x to x to get -9x.
z=-5x-3y+14_-9x-3y-6y+28=-8_14x-2y+3(-5x-3y+14)=-22
Since -3y and -6y are like terms, subtract 6y from -3y to get -9y.
z=-5x-3y+14_-9x-9y+28=-8_14x-2y+3(-5x-3y+14)=-22
Multiply 3 by each term inside the parentheses.
z=-5x-3y+14_-9x-9y+28=-8_14x-2y-15x-9y+42=-22
Since 14x and -15x are like terms, add -15x to 14x to get -x.
z=-5x-3y+14_-9x-9y+28=-8_-x-2y-9y+42=-22
Since -2y and -9y are like terms, subtract 9y from -2y to get -11y.
z=-5x-3y+14_-9x-9y+28=-8_-x-11y+42=-22
Move all terms not containing x to the right-hand side of the equation.
z=-5x-3y+14_-9x-9y+28=-8_-x=11y-42-22
Subtract 22 from -42 to get -64.
z=-5x-3y+14_-9x-9y+28=-8_-x=11y-64
Multiply each term in the equation by -1.
z=-5x-3y+14_-9x-9y+28=-8_-x*-1=11y*-1-64*-1
Multiply -x by -1 to get x.
z=-5x-3y+14_-9x-9y+28=-8_x=11y*-1-64*-1
Simplify the right-hand side of the equation by multiplying out all the terms.
z=-5x-3y+14_-9x-9y+28=-8_x=-11y+64
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -11y+64.
z=-5x-3y+14_-9(-11y+64)-9y+28=-8_x=-11y+64
Multiply -9 by each term inside the parentheses.
z=-5x-3y+14_99y-576-9y+28=-8_x=-11y+64
Since 99y and -9y are like terms, add -9y to 99y to get 90y.
z=-5x-3y+14_90y-576+28=-8_x=-11y+64
Add 28 to -576 to get -548.
z=-5x-3y+14_90y-548=-8_x=-11y+64
Since -548 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 548 to both sides.
z=-5x-3y+14_90y=548-8_x=-11y+64
Subtract 8 from 548 to get 540.
z=-5x-3y+14_90y=540_x=-11y+64
Divide each term in the equation by 90.
z=-5x-3y+14_(90y)/(90)=(540)/(90)_x=-11y+64
Simplify the left-hand side of the equation by canceling the common factors.
z=-5x-3y+14_y=(540)/(90)_x=-11y+64
Simplify the right-hand side of the equation by simplifying each term.
z=-5x-3y+14_y=6_x=-11y+64
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 6.
z=-5x-3(6)+14_y=6_x=-11y+64
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 6.
z=-5x-3(6)+14_y=6_x=-11(6)+64
Multiply -3 by each term inside the parentheses.
z=-5x-18+14_y=6_x=-11(6)+64
Add 14 to -18 to get -4.
z=-5x-4_y=6_x=-11(6)+64
Multiply -11 by each term inside the parentheses.
z=-5x-4_y=6_x=-66+64
Add 64 to -66 to get -2.
z=-5x-4_y=6_x=-2
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -2.
z=-5(-2)-4_y=6_x=-2
Multiply -5 by each term inside the parentheses.
z=10-4_y=6_x=-2
Subtract 4 from 10 to get 6.
z=6_y=6_x=-2
This is the solution to the system of equations.
z=6_y=6_x=-2
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