Solve {l}{2x+5y=9}{3y+2=10}

$$\left. \begin{array} { l } { 2 x + 5 y = 9 } \\ { 3 y + 2 = 10 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{13}{6} = -2\frac{1}{6} \approx -2.166666667$$

$$y = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

Solution Steps

Consider the second equation. Subtract 2 from both sides.

$$3y=10-2$$

Subtract 2 from 10 to get 8.

$$3y=8$$

Divide both sides by 3.

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

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

$$2x+5\times \frac{8}{3}=9$$

Multiply 5 and \frac{8}{3} to get \frac{40}{3}.

$$2x+\frac{40}{3}=9$$

Subtract \frac{40}{3} from both sides.

$$2x=9-\frac{40}{3}$$

Subtract \frac{40}{3} from 9 to get -\frac{13}{3}.

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

Divide both sides by 2.

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

Express \frac{-\frac{13}{3}}{2} as a single fraction.

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

Multiply 3 and 2 to get 6.

$$x=\frac{-13}{6}$$

Fraction \frac{-13}{6} can be rewritten as -\frac{13}{6} by extracting the negative sign.

$$x=-\frac{13}{6}$$

The system is now solved.

$$x=-\frac{13}{6} y=\frac{8}{3}$$