Solve {l}{5x+2y-2z=-1}{2x=7}{-4x+y=-21}

$$\left. \begin{array}{l}{ 5 x + 2 y - 2 z = - 1 }\\{ 2 x = 7 }\\{ - 4 x + y = - 21 }\end{array} \right.$$

Solve for x, y, z

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

$$y=-7$$

$$z = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

Solution Steps

Consider the second equation. Divide both sides by 2.

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

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

$$-4\times \frac{7}{2}+y=-21$$

Multiply -4 and \frac{7}{2} to get -14.

$$-14+y=-21$$

Add 14 to both sides.

$$y=-21+14$$

Add -21 and 14 to get -7.

$$y=-7$$

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

$$5\times \frac{7}{2}+2\left(-7\right)-2z=-1$$

Multiply 5 and \frac{7}{2} to get \frac{35}{2}.

$$\frac{35}{2}+2\left(-7\right)-2z=-1$$

Multiply 2 and -7 to get -14.

$$\frac{35}{2}-14-2z=-1$$

Subtract 14 from \frac{35}{2} to get \frac{7}{2}.

$$\frac{7}{2}-2z=-1$$

Subtract \frac{7}{2} from both sides.

$$-2z=-1-\frac{7}{2}$$

Subtract \frac{7}{2} from -1 to get -\frac{9}{2}.

$$-2z=-\frac{9}{2}$$

Divide both sides by -2.

$$z=\frac{-\frac{9}{2}}{-2}$$

Express \frac{-\frac{9}{2}}{-2} as a single fraction.

$$z=\frac{-9}{2\left(-2\right)}$$

Multiply 2 and -2 to get -4.

$$z=\frac{-9}{-4}$$

Fraction \frac{-9}{-4} can be simplified to \frac{9}{4} by removing the negative sign from both the numerator and the denominator.

$$z=\frac{9}{4}$$

The system is now solved.

$$x=\frac{7}{2} y=-7 z=\frac{9}{4}$$