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

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

Solve for x, y

$$x=\frac{1}{2}=0.5$$

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

Solution Steps

Consider the first equation. Subtract 3 from both sides.

$$2x=4-3$$

Subtract 3 from 4 to get 1.

$$2x=1$$

Divide both sides by 2.

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

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

$$3y+\frac{1}{2}=5$$

Subtract \frac{1}{2} from both sides.

$$3y=5-\frac{1}{2}$$

Subtract \frac{1}{2} from 5 to get \frac{9}{2}.

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

Divide both sides by 3.

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

Express \frac{\frac{9}{2}}{3} as a single fraction.

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

Multiply 2 and 3 to get 6.

$$y=\frac{9}{6}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

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

The system is now solved.

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