Solve {l}{5{(7x-53)}+6=3}{y={(-7x-3)}{(-11+2x)}}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 5 {(7 x - 53)} + 6 = 3 }\\ { y = {(-7 x - 3)} {(-11 + 2 x)} }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z, a

$$a = -\frac{38503}{175} = -220\frac{3}{175} \approx -220.017142857$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 5 by 7x-53.

$$35x-265+6=3$$

Add -265 and 6 to get -259.

$$35x-259=3$$

Add 259 to both sides.

$$35x=3+259$$

Add 3 and 259 to get 262.

$$35x=262$$

Divide both sides by 35.

$$x=\frac{262}{35}$$

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

$$y=\left(-7\times \frac{262}{35}-3\right)\left(-11+2\times \frac{262}{35}\right)$$

Multiply -7 and \frac{262}{35} to get -\frac{262}{5}.

$$y=\left(-\frac{262}{5}-3\right)\left(-11+2\times \frac{262}{35}\right)$$

Subtract 3 from -\frac{262}{5} to get -\frac{277}{5}.

$$y=-\frac{277}{5}\left(-11+2\times \frac{262}{35}\right)$$

Multiply 2 and \frac{262}{35} to get \frac{524}{35}.

$$y=-\frac{277}{5}\left(-11+\frac{524}{35}\right)$$

Add -11 and \frac{524}{35} to get \frac{139}{35}.

$$y=-\frac{277}{5}\times \frac{139}{35}$$

Multiply -\frac{277}{5} and \frac{139}{35} to get -\frac{38503}{175}.

$$y=-\frac{38503}{175}$$

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

$$z=-\frac{38503}{175}$$

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

$$a=-\frac{38503}{175}$$

The system is now solved.

$$x=\frac{262}{35} y=-\frac{38503}{175} z=-\frac{38503}{175} a=-\frac{38503}{175}$$