Solve {l}{{(5x-2{(2x+1)})}=2{(1-3y)}}{3/3+2y=1/2}{z={(2)}-1}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { {(5 x - 2 {(2 x + 1)})} = 2 {(1 - 3 y)} }\\ { \frac{3}{3} + 2 y = \frac{1}{2} }\\ { z = {(2)} - 1 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z, a

$$a=1$$

Solution Steps

Consider the second equation. Divide 3 by 3 to get 1.

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

Subtract 1 from both sides.

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

Subtract 1 from \frac{1}{2} to get -\frac{1}{2}.

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

Divide both sides by 2.

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

Express \frac{-\frac{1}{2}}{2} as a single fraction.

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

Multiply 2 and 2 to get 4.

$$y=\frac{-1}{4}$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$y=-\frac{1}{4}$$

Consider the third equation. Subtract 1 from 2 to get 1.

$$z=1$$

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

$$a=1$$

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

$$5x-2\left(2x+1\right)=2\left(1-3\left(-\frac{1}{4}\right)\right)$$

Use the distributive property to multiply -2 by 2x+1.

$$5x-4x-2=2\left(1-3\left(-\frac{1}{4}\right)\right)$$

Combine 5x and -4x to get x.

$$x-2=2\left(1-3\left(-\frac{1}{4}\right)\right)$$

Multiply -3 and -\frac{1}{4} to get \frac{3}{4}.

$$x-2=2\left(1+\frac{3}{4}\right)$$

Add 1 and \frac{3}{4} to get \frac{7}{4}.

$$x-2=2\times \frac{7}{4}$$

Multiply 2 and \frac{7}{4} to get \frac{7}{2}.

$$x-2=\frac{7}{2}$$

Add 2 to both sides.

$$x=\frac{7}{2}+2$$

Add \frac{7}{2} and 2 to get \frac{11}{2}.

$$x=\frac{11}{2}$$

The system is now solved.

$$x=\frac{11}{2} y=-\frac{1}{4} z=1 a=1$$