Solve for \(y\) in \(2x-y+z=5\).
Solve for \(y\).
\[2x-y+z=5\]
Subtract \(2x\) from both sides.
\[-y+z=5-2x\]
Regroup terms.
\[z-y=5-2x\]
Subtract \(z\) from both sides.
\[-y=5-2x-z\]
Multiply both sides by \(-1\).
\[y=-5+2x+z\]
\[y=-5+2x+z\]
Substitute \(y=-5+2x+z\) into \(4x+2y+3z=8\).
Start with the original equation.
\[4x+2y+3z=8\]
Let \(y=-5+2x+z\).
\[4x+2(-5+2x+z)+3z=8\]
Simplify.
\[8x-10+5z=8\]
\[8x-10+5z=8\]
Substitute \(y=-5+2x+z\) into \(3x-4y-z=3\).
Start with the original equation.
\[3x-4y-z=3\]
Let \(y=-5+2x+z\).
\[3x-4(-5+2x+z)-z=3\]
Simplify.
\[-5x+20-5z=3\]
\[-5x+20-5z=3\]
Solve for \(x\) in \(8x-10+5z=8\).
Solve for \(x\).
\[8x-10+5z=8\]
Add \(10\) to both sides.
\[8x+5z=8+10\]
Simplify \(8+10\) to \(18\).
\[8x+5z=18\]
Subtract \(5z\) from both sides.
\[8x=18-5z\]
Divide both sides by \(8\).
\[x=\frac{18-5z}{8}\]
\[x=\frac{18-5z}{8}\]
Substitute \(x=\frac{18-5z}{8}\) into \(y=-5+2x+z\).
Start with the original equation.
\[y=-5+2x+z\]
Let \(x=\frac{18-5z}{8}\).
\[y=-5+2\times \frac{18-5z}{8}+z\]
Simplify.
\[y=-5+\frac{18-5z}{4}+z\]
\[y=-5+\frac{18-5z}{4}+z\]
Substitute \(x=\frac{18-5z}{8}\) into \(-5x+20-5z=3\).
Start with the original equation.
\[-5x+20-5z=3\]
Let \(x=\frac{18-5z}{8}\).
\[-5\times \frac{18-5z}{8}+20-5z=3\]
Simplify.
\[-\frac{5(18-5z)}{8}+20-5z=3\]
\[-\frac{5(18-5z)}{8}+20-5z=3\]
Solve for \(z\) in \(-\frac{5(18-5z)}{8}+20-5z=3\).
Solve for \(z\).
\[-\frac{5(18-5z)}{8}+20-5z=3\]
Multiply both sides by \(8\).
\[-5(18-5z)+160-40z=24\]
Expand.
\[-90+25z+160-40z=24\]
Simplify \(-90+25z+160-40z\) to \(70-15z\).
\[70-15z=24\]
Subtract \(70\) from both sides.
\[-15z=24-70\]
Simplify \(24-70\) to \(-46\).
\[-15z=-46\]
Divide both sides by \(-15\).
\[z=\frac{-46}{-15}\]
Two negatives make a positive.
\[z=\frac{46}{15}\]
\[z=\frac{46}{15}\]
Substitute \(z=\frac{46}{15}\) into \(y=-5+\frac{18-5z}{4}+z\).
Start with the original equation.
\[y=-5+\frac{18-5z}{4}+z\]
Let \(z=\frac{46}{15}\).
\[y=-5+\frac{18-5\times \frac{46}{15}}{4}+\frac{46}{15}\]
Simplify.
\[y=-\frac{19}{15}\]
\[y=-\frac{19}{15}\]
Substitute \(z=\frac{46}{15}\) into \(x=\frac{18-5z}{8}\).
Start with the original equation.
\[x=\frac{18-5z}{8}\]
Let \(z=\frac{46}{15}\).
\[x=\frac{18-5\times \frac{46}{15}}{8}\]
Simplify.
\[x=\frac{1}{3}\]
\[x=\frac{1}{3}\]
Therefore,
\[\begin{aligned}&x=\frac{1}{3}\\&y=-\frac{19}{15}\\&z=\frac{46}{15}\end{aligned}\]
x=1/3;y=-19/15;z=46/15
