SOLUTION: 4x+y=-7 x-2z=4 3y+2z=8

Question 368882: 4x+y=-7
x-2z=4
3y+2z=8

Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
4x+y=-7_x-2z=4_3y+2z=8
Since 4x does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 4x from both sides.
y=-4x-7_x-2z=4_3y+2z=8
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is -4x-7.
y=-4x-7_x-2z=4_3y+2z=8
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is -4x-7.
y=-4x-7_x-2z=4_3(-4x-7)+2z=8
Multiply 3 by each term inside the parentheses.
y=-4x-7_x-2z=4_-12x-21+2z=8
Since -2z does not contain the variable to solve for, move it to the right-hand side of the equation by adding 2z to both sides.
y=-4x-7_x=2z+4_-12x+2z-21=8
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is 2z+4.
y=-4x-7_x=2z+4_-12(2z+4)+2z-21=8
Multiply -12 by each term inside the parentheses.
y=-4x-7_x=2z+4_-24z-48+2z-21=8
Since -24z and 2z are like terms, subtract 2z from -24z to get -22z.
y=-4x-7_x=2z+4_-22z-48-21=8
Subtract 21 from -48 to get -69.
y=-4x-7_x=2z+4_-22z-69=8
Since -69 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 69 to both sides.
y=-4x-7_x=2z+4_-22z=69+8
Add 8 to 69 to get 77.
y=-4x-7_x=2z+4_-22z=77
Divide each term in the equation by -22.
y=-4x-7_x=2z+4_-(22z)/(-22)=(77)/(-22)
Simplify the left-hand side of the equation by canceling the common factors.
y=-4x-7_x=2z+4_z=(77)/(-22)
Simplify the right-hand side of the equation by simplifying each term.
y=-4x-7_x=2z+4_z=-(7)/(2)
Replace all occurrences of z with the solution found by solving the last equation for z. In this case, the value substituted is -(7)/(2).
y=-4x-7_x=2z+4_z=-(7)/(2)
Replace all occurrences of z with the solution found by solving the last equation for z. In this case, the value substituted is -(7)/(2).
y=-4x-7_x=2(-(7)/(2))+4_z=-(7)/(2)
Multiply 2 by each term inside the parentheses.
y=-4x-7_x=-7+4_z=-(7)/(2)
Add 4 to -7 to get -3.
y=-4x-7_x=-3_z=-(7)/(2)
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -3.
y=-4(-3)-7_x=-3_z=-(7)/(2)
Multiply -4 by each term inside the parentheses.
y=12-7_x=-3_z=-(7)/(2)
Subtract 7 from 12 to get 5.
y=5_x=-3_z=-(7)/(2)
This is the solution to the system of equations.
y=5_x=-3_z=-(7)/(2)
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