Solve {l}{2x+y-3z=-2}{3y-z=3}{z=2}

$$\left\{ \begin{array} { l } { 2 x + y - 3 z = - 2 } \\ { 3 y - z = 3 } \\ { z = 2 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

$$y = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

$$z=2$$

Solution Steps

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

$$3y-2=3$$

Add 2 to both sides.

$$3y=3+2$$

Add 3 and 2 to get 5.

$$3y=5$$

Divide both sides by 3.

$$y=\frac{5}{3}$$

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

$$2x+\frac{5}{3}-3\times 2=-2$$

Multiply -3 and 2 to get -6.

$$2x+\frac{5}{3}-6=-2$$

Subtract 6 from \frac{5}{3} to get -\frac{13}{3}.

$$2x-\frac{13}{3}=-2$$

Add \frac{13}{3} to both sides.

$$2x=-2+\frac{13}{3}$$

Add -2 and \frac{13}{3} to get \frac{7}{3}.

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

Divide both sides by 2.

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

Express \frac{\frac{7}{3}}{2} as a single fraction.

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

Multiply 3 and 2 to get 6.

$$x=\frac{7}{6}$$

The system is now solved.

$$x=\frac{7}{6} y=\frac{5}{3} z=2$$