Solve {l}{36x-y+y=-14}{24x-17y=10}

$$\left. \begin{array} { l } { 36 x - y + y = - 14 } \\ { 24 x - 17 y = 10 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{7}{18}\approx -0.388888889$$

$$y = -\frac{58}{51} = -1\frac{7}{51} \approx -1.137254902$$

Solution Steps

Consider the first equation. Combine -y and y to get 0.

$$36x=-14$$

Divide both sides by 36.

$$x=\frac{-14}{36}$$

Reduce the fraction \frac{-14}{36} to lowest terms by extracting and canceling out 2.

$$x=-\frac{7}{18}$$

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

$$24\left(-\frac{7}{18}\right)-17y=10$$

Multiply 24 and -\frac{7}{18} to get -\frac{28}{3}.

$$-\frac{28}{3}-17y=10$$

Add \frac{28}{3} to both sides.

$$-17y=10+\frac{28}{3}$$

Add 10 and \frac{28}{3} to get \frac{58}{3}.

$$-17y=\frac{58}{3}$$

Divide both sides by -17.

$$y=\frac{\frac{58}{3}}{-17}$$

Express \frac{\frac{58}{3}}{-17} as a single fraction.

$$y=\frac{58}{3\left(-17\right)}$$

Multiply 3 and -17 to get -51.

$$y=\frac{58}{-51}$$

Fraction \frac{58}{-51} can be rewritten as -\frac{58}{51} by extracting the negative sign.

$$y=-\frac{58}{51}$$

The system is now solved.

$$x=-\frac{7}{18} y=-\frac{58}{51}$$