Solve for x, y, z
x=3
y=-2
z=5
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z=2x+3y+5
Solve 2x+3y-z=-5 for z.
x-4y+2\left(2x+3y+5\right)=21 5x+2y-3\left(2x+3y+5\right)=-4
Substitute 2x+3y+5 for z in the second and third equation.
y=-\frac{5}{2}x+\frac{11}{2} x=-7y-11
Solve these equations for y and x respectively.
x=-7\left(-\frac{5}{2}x+\frac{11}{2}\right)-11
Substitute -\frac{5}{2}x+\frac{11}{2} for y in the equation x=-7y-11.
x=3
Solve x=-7\left(-\frac{5}{2}x+\frac{11}{2}\right)-11 for x.
y=-\frac{5}{2}\times 3+\frac{11}{2}
Substitute 3 for x in the equation y=-\frac{5}{2}x+\frac{11}{2}.
y=-2
Calculate y from y=-\frac{5}{2}\times 3+\frac{11}{2}.
z=2\times 3+3\left(-2\right)+5
Substitute -2 for y and 3 for x in the equation z=2x+3y+5.
z=5
Calculate z from z=2\times 3+3\left(-2\right)+5.
x=3 y=-2 z=5
The system is now solved.
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