Solve {l}{x+3x=2}{x-y=8}

$$\left\{ \begin{array} { l } { x + 3 x = 2 } \\ { x - y = 8 } \end{array} \right.$$

Solve for x, y

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

$$y = -\frac{15}{2} = -7\frac{1}{2} = -7.5$$

Solution Steps

Consider the first equation. Combine x and 3x to get 4x.

$$4x=2$$

Divide both sides by 4.

$$x=\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

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

$$\frac{1}{2}-y=8$$

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

$$-y=8-\frac{1}{2}$$

Subtract \frac{1}{2} from 8 to get \frac{15}{2}.

$$-y=\frac{15}{2}$$

Divide both sides by -1.

$$y=\frac{\frac{15}{2}}{-1}$$

Express \frac{\frac{15}{2}}{-1} as a single fraction.

$$y=\frac{15}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$y=\frac{15}{-2}$$

Fraction \frac{15}{-2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$y=-\frac{15}{2}$$

The system is now solved.

$$x=\frac{1}{2} y=-\frac{15}{2}$$