Solve {l}{-11x+3200/9=-1}{y=75x+450}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{-11 x + 3200}{9} = -1 }\\ { y = 75 x + 450 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{245625}{11} = 22329\frac{6}{11} \approx 22329.545454545$$

Solution Steps

Consider the first equation. Multiply both sides by 9.

$$-11x+3200=-9$$

Subtract 3200 from both sides.

$$-11x=-9-3200$$

Subtract 3200 from -9 to get -3209.

$$-11x=-3209$$

Divide both sides by -11.

$$x=\frac{-3209}{-11}$$

Fraction \frac{-3209}{-11} can be simplified to \frac{3209}{11} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{3209}{11}$$

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

$$y=75\times \frac{3209}{11}+450$$

Multiply 75 and \frac{3209}{11} to get \frac{240675}{11}.

$$y=\frac{240675}{11}+450$$

Add \frac{240675}{11} and 450 to get \frac{245625}{11}.

$$y=\frac{245625}{11}$$

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

$$z=\frac{245625}{11}$$

The system is now solved.

$$x=\frac{3209}{11} y=\frac{245625}{11} z=\frac{245625}{11}$$