Solve for x, z, y
x=10
y=15
z=25
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x=-\frac{3}{4}z+\frac{115}{4}
Solve 4x+3z=115 for x.
5\left(-\frac{3}{4}z+\frac{115}{4}\right)+6y=140
Substitute -\frac{3}{4}z+\frac{115}{4} for x in the equation 5x+6y=140.
z=-\frac{7}{5}y+46 y=-\frac{5}{8}+\frac{5}{8}z
Solve the second equation for z and the third equation for y.
y=-\frac{5}{8}+\frac{5}{8}\left(-\frac{7}{5}y+46\right)
Substitute -\frac{7}{5}y+46 for z in the equation y=-\frac{5}{8}+\frac{5}{8}z.
y=15
Solve y=-\frac{5}{8}+\frac{5}{8}\left(-\frac{7}{5}y+46\right) for y.
z=-\frac{7}{5}\times 15+46
Substitute 15 for y in the equation z=-\frac{7}{5}y+46.
z=25
Calculate z from z=-\frac{7}{5}\times 15+46.
x=-\frac{3}{4}\times 25+\frac{115}{4}
Substitute 25 for z in the equation x=-\frac{3}{4}z+\frac{115}{4}.
x=10
Calculate x from x=-\frac{3}{4}\times 25+\frac{115}{4}.
x=10 z=25 y=15
The system is now solved.
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