{l}{4x+2=8}{2x+y=x/8}-এর সমাধান করুন

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

Solve for x, y

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

$$y = -\frac{45}{16} = -2\frac{13}{16} = -2.8125$$

Solution Steps

Consider the first equation. Subtract 2 from both sides.

$$4x=8-2$$

Subtract 2 from 8 to get 6.

$$4x=6$$

Divide both sides by 4.

$$x=\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

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

$$2\times \frac{3}{2}+y=\frac{\frac{3}{2}}{8}$$

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

$$3+y=\frac{\frac{3}{2}}{8}$$

Express \frac{\frac{3}{2}}{8} as a single fraction.

$$3+y=\frac{3}{2\times 8}$$

Multiply 2 and 8 to get 16.

$$3+y=\frac{3}{16}$$

Subtract 3 from both sides.

$$y=\frac{3}{16}-3$$

Subtract 3 from \frac{3}{16} to get -\frac{45}{16}.

$$y=-\frac{45}{16}$$

The system is now solved.

$$x=\frac{3}{2} y=-\frac{45}{16}$$