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

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

Solve for x, y

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

$$y = \frac{16}{9} = 1\frac{7}{9} \approx 1.777777778$$

Solution Steps

Consider the first equation. Add 2 to both sides. Anything plus zero gives itself.

$$3x=2$$

Divide both sides by 3.

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

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

$$y=\left(\frac{2}{3}\right)^{2}+2\times \frac{2}{3}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$y=\frac{4}{9}+2\times \frac{2}{3}$$

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

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

Add \frac{4}{9} and \frac{4}{3} to get \frac{16}{9}.

$$y=\frac{16}{9}$$

The system is now solved.

$$x=\frac{2}{3} y=\frac{16}{9}$$