Solve {r}{-2y-3x=7}{9y+5y=-2}

$$\left. \begin{array} { r } { - 2 y - 3 x = 7 } \\ { 9 y + 5 y = - 2 } \end{array} \right.$$

Solve for y, x

$$x = -\frac{47}{21} = -2\frac{5}{21} \approx -2.238095238$$

$$y=-\frac{1}{7}\approx -0.142857143$$

Solution Steps

Consider the second equation. Combine 9y and 5y to get 14y.

$$14y=-2$$

Divide both sides by 14.

$$y=\frac{-2}{14}$$

Reduce the fraction \frac{-2}{14} to lowest terms by extracting and canceling out 2.

$$y=-\frac{1}{7}$$

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

$$-2\left(-\frac{1}{7}\right)-3x=7$$

Multiply -2 and -\frac{1}{7} to get \frac{2}{7}.

$$\frac{2}{7}-3x=7$$

Subtract \frac{2}{7} from both sides.

$$-3x=7-\frac{2}{7}$$

Subtract \frac{2}{7} from 7 to get \frac{47}{7}.

$$-3x=\frac{47}{7}$$

Divide both sides by -3.

$$x=\frac{\frac{47}{7}}{-3}$$

Express \frac{\frac{47}{7}}{-3} as a single fraction.

$$x=\frac{47}{7\left(-3\right)}$$

Multiply 7 and -3 to get -21.

$$x=\frac{47}{-21}$$

Fraction \frac{47}{-21} can be rewritten as -\frac{47}{21} by extracting the negative sign.

$$x=-\frac{47}{21}$$

The system is now solved.

$$y=-\frac{1}{7} x=-\frac{47}{21}$$