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

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

Solve for x, y

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$y=-\frac{5}{8}=-0.625$$

Solution Steps

Consider the first equation. Subtract 5 from both sides.

$$2x=8-5$$

Subtract 5 from 8 to get 3.

$$2x=3$$

Divide both sides by 2.

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

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

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

Multiply 3 and \frac{3}{2} to get \frac{9}{2}.

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

Subtract \frac{9}{2} from both sides.

$$4y=2-\frac{9}{2}$$

Subtract \frac{9}{2} from 2 to get -\frac{5}{2}.

$$4y=-\frac{5}{2}$$

Divide both sides by 4.

$$y=\frac{-\frac{5}{2}}{4}$$

Express \frac{-\frac{5}{2}}{4} as a single fraction.

$$y=\frac{-5}{2\times 4}$$

Multiply 2 and 4 to get 8.

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

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

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

The system is now solved.

$$x=\frac{3}{2} y=-\frac{5}{8}$$