Solve {l}{x+y=2z}{x-y=29}{7x=51}

$$\left. \begin{array} { l } { x + y = 2 z } \\ { x - y = 29 } \\ { 7 x = 51 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{51}{7} = 7\frac{2}{7} \approx 7.285714286$$

$$y = -\frac{152}{7} = -21\frac{5}{7} \approx -21.714285714$$

$$z = -\frac{101}{14} = -7\frac{3}{14} \approx -7.214285714$$

Solution Steps

Consider the third equation. Divide both sides by 7.

$$x=\frac{51}{7}$$

Consider the second equation. Insert the known values of variables into the equation.

$$\frac{51}{7}-y=29$$

Subtract \frac{51}{7} from both sides.

$$-y=29-\frac{51}{7}$$

Subtract \frac{51}{7} from 29 to get \frac{152}{7}.

$$-y=\frac{152}{7}$$

Divide both sides by -1.

$$y=\frac{\frac{152}{7}}{-1}$$

Express \frac{\frac{152}{7}}{-1} as a single fraction.

$$y=\frac{152}{7\left(-1\right)}$$

Multiply 7 and -1 to get -7.

$$y=\frac{152}{-7}$$

Fraction \frac{152}{-7} can be rewritten as -\frac{152}{7} by extracting the negative sign.

$$y=-\frac{152}{7}$$

Consider the first equation. Insert the known values of variables into the equation.

$$\frac{51}{7}-\frac{152}{7}=2z$$

Subtract \frac{152}{7} from \frac{51}{7} to get -\frac{101}{7}.

$$-\frac{101}{7}=2z$$

Swap sides so that all variable terms are on the left hand side.

$$2z=-\frac{101}{7}$$

Divide both sides by 2.

$$z=\frac{-\frac{101}{7}}{2}$$

Express \frac{-\frac{101}{7}}{2} as a single fraction.

$$z=\frac{-101}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$z=\frac{-101}{14}$$

Fraction \frac{-101}{14} can be rewritten as -\frac{101}{14} by extracting the negative sign.

$$z=-\frac{101}{14}$$

The system is now solved.

$$x=\frac{51}{7} y=-\frac{152}{7} z=-\frac{101}{14}$$