Solve {l}{2/3x+1=-6}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{2}{3} x + 1 = -6 }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = -\frac{21}{2} = -10\frac{1}{2} = -10.5$$

Solution Steps

Consider the first equation. Subtract 1 from both sides.

$$\frac{2}{3}x=-6-1$$

Subtract 1 from -6 to get -7.

$$\frac{2}{3}x=-7$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$x=-7\times \frac{3}{2}$$

Multiply -7 and \frac{3}{2} to get -\frac{21}{2}.

$$x=-\frac{21}{2}$$

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

$$y=-\frac{21}{2}$$

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

$$z=-\frac{21}{2}$$

The system is now solved.

$$x=-\frac{21}{2} y=-\frac{21}{2} z=-\frac{21}{2}$$