Solve {l}{x+y=15}{10x=8-2}{15x=z+5}

$$\left\{ \begin{array} { l } { x + y = 15 } \\ { 10 x = 8 - 2 } \\ { 15 x = z + 5 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{3}{5}=0.6$$

$$y = \frac{72}{5} = 14\frac{2}{5} = 14.4$$

$$z=4$$

Solution Steps

Consider the second equation. Subtract 2 from 8 to get 6.

$$10x=6$$

Divide both sides by 10.

$$x=\frac{6}{10}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

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

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

$$15\times \frac{3}{5}=z+5$$

Multiply 15 and \frac{3}{5} to get 9.

$$9=z+5$$

Swap sides so that all variable terms are on the left hand side.

$$z+5=9$$

Subtract 5 from both sides.

$$z=9-5$$

Subtract 5 from 9 to get 4.

$$z=4$$

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

$$\frac{3}{5}+y=15$$

Subtract \frac{3}{5} from both sides.

$$y=15-\frac{3}{5}$$

Subtract \frac{3}{5} from 15 to get \frac{72}{5}.

$$y=\frac{72}{5}$$

The system is now solved.

$$x=\frac{3}{5} y=\frac{72}{5} z=4$$