Solve {c}{-5x+4=-13}{2x-y=7}

$$\left. \begin{array} { c } { - 5 x + 4 = - 13 } \\ { 2 x - y = 7 } \end{array} \right.$$

Solve for x, y

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

$$y=-\frac{1}{5}=-0.2$$

Solution Steps

Consider the first equation. Subtract 4 from both sides.

$$-5x=-13-4$$

Subtract 4 from -13 to get -17.

$$-5x=-17$$

Divide both sides by -5.

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

Fraction \frac{-17}{-5} can be simplified to \frac{17}{5} by removing the negative sign from both the numerator and the denominator.

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

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

$$2\times \frac{17}{5}-y=7$$

Multiply 2 and \frac{17}{5} to get \frac{34}{5}.

$$\frac{34}{5}-y=7$$

Subtract \frac{34}{5} from both sides.

$$-y=7-\frac{34}{5}$$

Subtract \frac{34}{5} from 7 to get \frac{1}{5}.

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

Divide both sides by -1.

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

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

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

Multiply 5 and -1 to get -5.

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

Fraction \frac{1}{-5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

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

The system is now solved.

$$x=\frac{17}{5} y=-\frac{1}{5}$$