Solve {l}{3y+2=0}{2x+y=1}

$$\left. \begin{array} { l } { 3 y + 2 = 0 } \\ { 2 x + y = 1 } \end{array} \right.$$

Solve for y, x

$$x=\frac{5}{6}\approx 0.833333333$$

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

Solution Steps

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

$$3y=-2$$

Divide both sides by 3.

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

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

$$2x-\frac{2}{3}=1$$

Add \frac{2}{3} to both sides.

$$2x=1+\frac{2}{3}$$

Add 1 and \frac{2}{3} to get \frac{5}{3}.

$$2x=\frac{5}{3}$$

Divide both sides by 2.

$$x=\frac{\frac{5}{3}}{2}$$

Express \frac{\frac{5}{3}}{2} as a single fraction.

$$x=\frac{5}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$x=\frac{5}{6}$$

The system is now solved.

$$y=-\frac{2}{3} x=\frac{5}{6}$$