Solve {l}{5x-6y=0}{7y-4=0}{z=-1}

$$\left. \begin{array} { l } { 5 x - 6 y = 0 } \\ { 7 y - 4 = 0 } \\ { z = - 1 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{24}{35}\approx 0.685714286$$

$$y=\frac{4}{7}\approx 0.571428571$$

$$z=-1$$

Solution Steps

Consider the second equation. Add 4 to both sides. Anything plus zero gives itself.

$$7y=4$$

Divide both sides by 7.

$$y=\frac{4}{7}$$

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

$$5x-6\times \frac{4}{7}=0$$

Multiply -6 and \frac{4}{7} to get -\frac{24}{7}.

$$5x-\frac{24}{7}=0$$

Add \frac{24}{7} to both sides. Anything plus zero gives itself.

$$5x=\frac{24}{7}$$

Divide both sides by 5.

$$x=\frac{\frac{24}{7}}{5}$$

Express \frac{\frac{24}{7}}{5} as a single fraction.

$$x=\frac{24}{7\times 5}$$

Multiply 7 and 5 to get 35.

$$x=\frac{24}{35}$$

The system is now solved.

$$x=\frac{24}{35} y=\frac{4}{7} z=-1$$