Solve {l}{6x+4=-9}{2x-3y=7}

$$\left\{ \begin{array} { l } { 6 x + 4 = - 9 } \\ { 2 x - 3 y = 7 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{13}{6} = -2\frac{1}{6} \approx -2.166666667$$

$$y = -\frac{34}{9} = -3\frac{7}{9} \approx -3.777777778$$

Solution Steps

Consider the first equation. Subtract 4 from both sides.

$$6x=-9-4$$

Subtract 4 from -9 to get -13.

$$6x=-13$$

Divide both sides by 6.

$$x=-\frac{13}{6}$$

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

$$2\left(-\frac{13}{6}\right)-3y=7$$

Multiply 2 and -\frac{13}{6} to get -\frac{13}{3}.

$$-\frac{13}{3}-3y=7$$

Add \frac{13}{3} to both sides.

$$-3y=7+\frac{13}{3}$$

Add 7 and \frac{13}{3} to get \frac{34}{3}.

$$-3y=\frac{34}{3}$$

Divide both sides by -3.

$$y=\frac{\frac{34}{3}}{-3}$$

Express \frac{\frac{34}{3}}{-3} as a single fraction.

$$y=\frac{34}{3\left(-3\right)}$$

Multiply 3 and -3 to get -9.

$$y=\frac{34}{-9}$$

Fraction \frac{34}{-9} can be rewritten as -\frac{34}{9} by extracting the negative sign.

$$y=-\frac{34}{9}$$

The system is now solved.

$$x=-\frac{13}{6} y=-\frac{34}{9}$$