Solve {l}{7x+2^2=0}{y={(7x+2)}{(11x+1)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 7 x + 2 ^ {2} = 0 }\\ { y = {(7 x + 2)} {(11 x + 1)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{74}{7} = 10\frac{4}{7} \approx 10.571428571$$

Solution Steps

Consider the first equation. Calculate 2 to the power of 2 and get 4.

$$7x+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$7x=-4$$

Divide both sides by 7.

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

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

$$y=\left(7\left(-\frac{4}{7}\right)+2\right)\left(11\left(-\frac{4}{7}\right)+1\right)$$

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

$$y=\left(-4+2\right)\left(11\left(-\frac{4}{7}\right)+1\right)$$

Add -4 and 2 to get -2.

$$y=-2\left(11\left(-\frac{4}{7}\right)+1\right)$$

Multiply 11 and -\frac{4}{7} to get -\frac{44}{7}.

$$y=-2\left(-\frac{44}{7}+1\right)$$

Add -\frac{44}{7} and 1 to get -\frac{37}{7}.

$$y=-2\left(-\frac{37}{7}\right)$$

Multiply -2 and -\frac{37}{7} to get \frac{74}{7}.

$$y=\frac{74}{7}$$

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

$$z=\frac{74}{7}$$

The system is now solved.

$$x=-\frac{4}{7} y=\frac{74}{7} z=\frac{74}{7}$$