Solve for x, y, z
x = \frac{16}{13} = 1\frac{3}{13} \approx 1.230769231
y=\frac{11}{13}\approx 0.846153846
z = \frac{103}{13} = 7\frac{12}{13} \approx 7.923076923
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5x+y=7 2x+3y=5 x+y+z=10
Reorder the equations.
y=-5x+7
Solve 5x+y=7 for y.
2x+3\left(-5x+7\right)=5 x-5x+7+z=10
Substitute -5x+7 for y in the second and third equation.
x=\frac{16}{13} z=4x+3
Solve these equations for x and z respectively.
z=4\times \frac{16}{13}+3
Substitute \frac{16}{13} for x in the equation z=4x+3.
z=\frac{103}{13}
Calculate z from z=4\times \frac{16}{13}+3.
y=-5\times \frac{16}{13}+7
Substitute \frac{16}{13} for x in the equation y=-5x+7.
y=\frac{11}{13}
Calculate y from y=-5\times \frac{16}{13}+7.
x=\frac{16}{13} y=\frac{11}{13} z=\frac{103}{13}
The system is now solved.
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