Solve {c}{5x+8y=9c}{x=4y}{c+y=6}

$$\left. \begin{array} { c } { 5 x + 8 y = 9 c } \\ { x = 4 y } \\ { c + y = 6 } \end{array} \right.$$

Solve for x, y, c

$$x = \frac{216}{37} = 5\frac{31}{37} \approx 5.837837838$$

$$y = \frac{54}{37} = 1\frac{17}{37} \approx 1.459459459$$

$$c = \frac{168}{37} = 4\frac{20}{37} \approx 4.540540541$$

Short Steps Using Substitution

Reorder the equations.

$$x=4y 5x+8y=9c c+y=6$$

Substitute 4y for x in the equation 5x+8y=9c.

$$5\times 4y+8y=9c$$

Solve the second equation for y and the third equation for c.

$$y=\frac{9}{28}c c=-y+6$$

Substitute \frac{9}{28}c for y in the equation c=-y+6.

$$c=-\frac{9}{28}c+6$$

Solve c=-\frac{9}{28}c+6 for c.

$$c=\frac{168}{37}$$

Substitute \frac{168}{37} for c in the equation y=\frac{9}{28}c.

$$y=\frac{9}{28}\times \frac{168}{37}$$

Calculate y from y=\frac{9}{28}\times \frac{168}{37}.

$$y=\frac{54}{37}$$

Substitute \frac{54}{37} for y in the equation x=4y.

$$x=4\times \frac{54}{37}$$

Calculate x from x=4\times \frac{54}{37}.

$$x=\frac{216}{37}$$

The system is now solved.

$$x=\frac{216}{37} y=\frac{54}{37} c=\frac{168}{37}$$