\left\{ \begin{array} { l } { 2 x = 3 y } \\ { 4 y = 5 z } \\ { x + y + z = 66 } \end{array} \right.
Solve for x, y, z
x=30
y=20
z=16
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x+y+z=66 4y=5z 2x=3y
Reorder the equations.
x=-y-z+66
Solve x+y+z=66 for x.
2\left(-y-z+66\right)=3y
Substitute -y-z+66 for x in the equation 2x=3y.
y=\frac{5}{4}z z=66-\frac{5}{2}y
Solve the second equation for y and the third equation for z.
z=66-\frac{5}{2}\times \frac{5}{4}z
Substitute \frac{5}{4}z for y in the equation z=66-\frac{5}{2}y.
z=16
Solve z=66-\frac{5}{2}\times \frac{5}{4}z for z.
y=\frac{5}{4}\times 16
Substitute 16 for z in the equation y=\frac{5}{4}z.
y=20
Calculate y from y=\frac{5}{4}\times 16.
x=-20-16+66
Substitute 20 for y and 16 for z in the equation x=-y-z+66.
x=30
Calculate x from x=-20-16+66.
x=30 y=20 z=16
The system is now solved.
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