Solve {l}{4x+5=7}{7x+3y=2}

$$\left\{ \begin{array} { l } { 4 x + 5 = 7 } \\ { 7 x + 3 y = 2 } \end{array} \right.$$

Solve for x, y

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

$$y=-\frac{1}{2}=-0.5$$

Solution Steps

Consider the first equation. Subtract 5 from both sides.

$$4x=7-5$$

Subtract 5 from 7 to get 2.

$$4x=2$$

Divide both sides by 4.

$$x=\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

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

$$7\times \frac{1}{2}+3y=2$$

Multiply 7 and \frac{1}{2} to get \frac{7}{2}.

$$\frac{7}{2}+3y=2$$

Subtract \frac{7}{2} from both sides.

$$3y=2-\frac{7}{2}$$

Subtract \frac{7}{2} from 2 to get -\frac{3}{2}.

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

Divide both sides by 3.

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

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

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

Multiply 2 and 3 to get 6.

$$y=\frac{-3}{6}$$

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

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

The system is now solved.

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