Solve {l}{2x+9y=-4}{3x+13=-7}

$$\left. \begin{array} { l } { 2 x + 9 y = - 4 } \\ { 3 x + 13 = - 7 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{20}{3} = -6\frac{2}{3} \approx -6.666666667$$

$$y = \frac{28}{27} = 1\frac{1}{27} \approx 1.037037037$$

Solution Steps

Consider the second equation. Subtract 13 from both sides.

$$3x=-7-13$$

Subtract 13 from -7 to get -20.

$$3x=-20$$

Divide both sides by 3.

$$x=-\frac{20}{3}$$

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

$$2\left(-\frac{20}{3}\right)+9y=-4$$

Multiply 2 and -\frac{20}{3} to get -\frac{40}{3}.

$$-\frac{40}{3}+9y=-4$$

Add \frac{40}{3} to both sides.

$$9y=-4+\frac{40}{3}$$

Add -4 and \frac{40}{3} to get \frac{28}{3}.

$$9y=\frac{28}{3}$$

Divide both sides by 9.

$$y=\frac{\frac{28}{3}}{9}$$

Express \frac{\frac{28}{3}}{9} as a single fraction.

$$y=\frac{28}{3\times 9}$$

Multiply 3 and 9 to get 27.

$$y=\frac{28}{27}$$

The system is now solved.

$$x=-\frac{20}{3} y=\frac{28}{27}$$