Solve {l}{2x-5y=12}{-3y=-9}{2x-3y+4z=8}

$$\left. \begin{array} { l } { 2 x - 5 y = 12 } \\ { - 3 y = - 9 } \\ { 2 x - 3 y + 4 z = 8 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{27}{2} = 13\frac{1}{2} = 13.5$$

$$y=3$$

$$z=\frac{17-t_{1744830465}}{4}$$

Solution Steps

Consider the second equation. Divide both sides by -3.

$$y=\frac{-9}{-3}$$

Divide -9 by -3 to get 3.

$$y=3$$

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

$$2x-5\times 3=12$$

Multiply -5 and 3 to get -15.

$$2x-15=12$$

Add 15 to both sides.

$$2x=12+15$$

Add 12 and 15 to get 27.

$$2x=27$$

Divide both sides by 2.

$$x=\frac{27}{2}$$

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

$$2\times \frac{27}{2}-3\times 3+4z=8$$

Multiply 2 and \frac{27}{2} to get 27.

$$27-3\times 3+4z=8$$

Multiply -3 and 3 to get -9.

$$27-9+4z=8$$

Subtract 9 from 27 to get 18.

$$18+4z=8$$

Subtract 18 from both sides.

$$4z=8-18$$

Subtract 18 from 8 to get -10.

$$4z=-10$$

Divide both sides by 4.

$$z=\frac{-10}{4}$$

Reduce the fraction \frac{-10}{4} to lowest terms by extracting and canceling out 2.

$$z=-\frac{5}{2}$$

The system is now solved.

$$x=\frac{27}{2} y=3 z=-\frac{5}{2}$$