Solve {l}{3x+2=0}{4x-2y=6}

$$\left\{ \begin{array} { l } { 3 x + 2 = 0 } \\ { 4 x - 2 y = 6 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{2}{3}\approx -0.666666667$$

$$y = -\frac{13}{3} = -4\frac{1}{3} \approx -4.333333333$$

Solution Steps

Consider the first equation. Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$3x=-2$$

Divide both sides by 3.

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

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

$$4\left(-\frac{2}{3}\right)-2y=6$$

Multiply 4 and -\frac{2}{3} to get -\frac{8}{3}.

$$-\frac{8}{3}-2y=6$$

Add \frac{8}{3} to both sides.

$$-2y=6+\frac{8}{3}$$

Add 6 and \frac{8}{3} to get \frac{26}{3}.

$$-2y=\frac{26}{3}$$

Divide both sides by -2.

$$y=\frac{\frac{26}{3}}{-2}$$

Express \frac{\frac{26}{3}}{-2} as a single fraction.

$$y=\frac{26}{3\left(-2\right)}$$

Multiply 3 and -2 to get -6.

$$y=\frac{26}{-6}$$

Reduce the fraction \frac{26}{-6} to lowest terms by extracting and canceling out 2.

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

The system is now solved.

$$x=-\frac{2}{3} y=-\frac{13}{3}$$