Solve {l}{3x+2x=17}{x-y=4}

$$\left\{ \begin{array} { l } { 3 x + 2 x = 17 } \\ { x - y = 4 } \end{array} \right.$$

Solve for x, y

$$x = \frac{17}{5} = 3\frac{2}{5} = 3.4$$

$$y=-\frac{3}{5}=-0.6$$

Solution Steps

Consider the first equation. Combine 3x and 2x to get 5x.

$$5x=17$$

Divide both sides by 5.

$$x=\frac{17}{5}$$

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

$$\frac{17}{5}-y=4$$

Subtract \frac{17}{5} from both sides.

$$-y=4-\frac{17}{5}$$

Subtract \frac{17}{5} from 4 to get \frac{3}{5}.

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

Divide both sides by -1.

$$y=\frac{\frac{3}{5}}{-1}$$

Express \frac{\frac{3}{5}}{-1} as a single fraction.

$$y=\frac{3}{5\left(-1\right)}$$

Multiply 5 and -1 to get -5.

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

Fraction \frac{3}{-5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

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

The system is now solved.

$$x=\frac{17}{5} y=-\frac{3}{5}$$