Solve {l}{6x+3x+9y=0}{3x+7=0}

$$\left\{ \begin{array} { l } { 6 x + 3 x + 9 y = 0 } \\ { 3 x + 7 = 0 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{7}{3} = -2\frac{1}{3} \approx -2.333333333$$

$$y = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Solution Steps

Consider the second equation. Subtract 7 from both sides. Anything subtracted from zero gives its negation.

$$3x=-7$$

Divide both sides by 3.

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

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

$$6\left(-\frac{7}{3}\right)+3\left(-\frac{7}{3}\right)+9y=0$$

Multiply 6 and -\frac{7}{3} to get -14.

$$-14+3\left(-\frac{7}{3}\right)+9y=0$$

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

$$-14-7+9y=0$$

Subtract 7 from -14 to get -21.

$$-21+9y=0$$

Add 21 to both sides. Anything plus zero gives itself.

$$9y=21$$

Divide both sides by 9.

$$y=\frac{21}{9}$$

Reduce the fraction \frac{21}{9} to lowest terms by extracting and canceling out 3.

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

The system is now solved.

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