Solve for x, y, z
x=2
y=3
z=5
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x+y+5z=30 3x+2y+4z=32 2x+3y+7z=48
Reorder the equations.
x=-y-5z+30
Solve x+y+5z=30 for x.
3\left(-y-5z+30\right)+2y+4z=32 2\left(-y-5z+30\right)+3y+7z=48
Substitute -y-5z+30 for x in the second and third equation.
y=-11z+58 z=\frac{1}{3}y+4
Solve these equations for y and z respectively.
z=\frac{1}{3}\left(-11z+58\right)+4
Substitute -11z+58 for y in the equation z=\frac{1}{3}y+4.
z=5
Solve z=\frac{1}{3}\left(-11z+58\right)+4 for z.
y=-11\times 5+58
Substitute 5 for z in the equation y=-11z+58.
y=3
Calculate y from y=-11\times 5+58.
x=-3-5\times 5+30
Substitute 3 for y and 5 for z in the equation x=-y-5z+30.
x=2
Calculate x from x=-3-5\times 5+30.
x=2 y=3 z=5
The system is now solved.
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