Solve {l}{2x+3y=5}{3x+4=8}

$$\left. \begin{array} { l } { 2 x + 3 y = 5 } \\ { 3 x + 4 = 8 } \end{array} \right.$$

Solve for x, y

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

$$y=\frac{7}{9}\approx 0.777777778$$

Solution Steps

Consider the second equation. Subtract 4 from both sides.

$$3x=8-4$$

Subtract 4 from 8 to get 4.

$$3x=4$$

Divide both sides by 3.

$$x=\frac{4}{3}$$

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

$$2\times \frac{4}{3}+3y=5$$

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

$$\frac{8}{3}+3y=5$$

Subtract \frac{8}{3} from both sides.

$$3y=5-\frac{8}{3}$$

Subtract \frac{8}{3} from 5 to get \frac{7}{3}.

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

Divide both sides by 3.

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

Express \frac{\frac{7}{3}}{3} as a single fraction.

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

Multiply 3 and 3 to get 9.

$$y=\frac{7}{9}$$

The system is now solved.

$$x=\frac{4}{3} y=\frac{7}{9}$$