Solve {l}{2x+2x+2x=35}{y+y+2x=20}{2z+2z+2z+y=1.7}

$$\left. \begin{array} { l } { 2 x + 2 x + 2 x = 35 } \\ { y + y + 2 x = 20 } \\ { 2 z + 2 z + 2 z + y = 1.7 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{35}{6} = 5\frac{5}{6} \approx 5.833333333$$

$$y = \frac{25}{6} = 4\frac{1}{6} \approx 4.166666667$$

$$z=-\frac{37}{90}\approx -0.411111111$$

Solution Steps

Consider the first equation. Combine 2x and 2x to get 4x.

$$4x+2x=35$$

Combine 4x and 2x to get 6x.

$$6x=35$$

Divide both sides by 6.

$$x=\frac{35}{6}$$

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

$$y+y+2\times \frac{35}{6}=20$$

Combine y and y to get 2y.

$$2y+2\times \frac{35}{6}=20$$

Multiply 2 and \frac{35}{6} to get \frac{35}{3}.

$$2y+\frac{35}{3}=20$$

Subtract \frac{35}{3} from both sides.

$$2y=20-\frac{35}{3}$$

Subtract \frac{35}{3} from 20 to get \frac{25}{3}.

$$2y=\frac{25}{3}$$

Divide both sides by 2.

$$y=\frac{\frac{25}{3}}{2}$$

Express \frac{\frac{25}{3}}{2} as a single fraction.

$$y=\frac{25}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$y=\frac{25}{6}$$

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

$$2z+2z+2z+\frac{25}{6}=1.7$$

Combine 2z and 2z to get 4z.

$$4z+2z+\frac{25}{6}=1.7$$

Combine 4z and 2z to get 6z.

$$6z+\frac{25}{6}=1.7$$

Subtract \frac{25}{6} from both sides.

$$6z=1.7-\frac{25}{6}$$

Subtract \frac{25}{6} from 1.7 to get -\frac{37}{15}.

$$6z=-\frac{37}{15}$$

Divide both sides by 6.

$$z=\frac{-\frac{37}{15}}{6}$$

Express \frac{-\frac{37}{15}}{6} as a single fraction.

$$z=\frac{-37}{15\times 6}$$

Multiply 15 and 6 to get 90.

$$z=\frac{-37}{90}$$

Fraction \frac{-37}{90} can be rewritten as -\frac{37}{90} by extracting the negative sign.

$$z=-\frac{37}{90}$$

The system is now solved.

$$x=\frac{35}{6} y=\frac{25}{6} z=-\frac{37}{90}$$