Solve {l}{x+y+y=6}{x-y-z=4}{2x-y+y=1}

$$\left\{ \begin{array} { l } { x + y + y = 6 } \\ { x - y - z = 4 } \\ { 2 x - y + y = 1 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{1}{2}=0.5$$

$$y = \frac{11}{4} = 2\frac{3}{4} = 2.75$$

$$z = -\frac{25}{4} = -6\frac{1}{4} = -6.25$$

Solution Steps

Consider the first equation. Combine y and y to get 2y.

$$x+2y=6$$

Consider the third equation. Combine -y and y to get 0.

$$2x=1$$

Divide both sides by 2.

$$x=\frac{1}{2}$$

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

$$\frac{1}{2}+2y=6$$

Subtract \frac{1}{2} from both sides.

$$2y=6-\frac{1}{2}$$

Subtract \frac{1}{2} from 6 to get \frac{11}{2}.

$$2y=\frac{11}{2}$$

Divide both sides by 2.

$$y=\frac{\frac{11}{2}}{2}$$

Express \frac{\frac{11}{2}}{2} as a single fraction.

$$y=\frac{11}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$y=\frac{11}{4}$$

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

$$\frac{1}{2}-\frac{11}{4}-z=4$$

Subtract \frac{11}{4} from \frac{1}{2} to get -\frac{9}{4}.

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

Add \frac{9}{4} to both sides.

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

Add 4 and \frac{9}{4} to get \frac{25}{4}.

$$-z=\frac{25}{4}$$

Divide both sides by -1.

$$z=\frac{\frac{25}{4}}{-1}$$

Express \frac{\frac{25}{4}}{-1} as a single fraction.

$$z=\frac{25}{4\left(-1\right)}$$

Multiply 4 and -1 to get -4.

$$z=\frac{25}{-4}$$

Fraction \frac{25}{-4} can be rewritten as -\frac{25}{4} by extracting the negative sign.

$$z=-\frac{25}{4}$$

The system is now solved.

$$x=\frac{1}{2} y=\frac{11}{4} z=-\frac{25}{4}$$