Solve {r}{1-14z=-350,000}{3y-7z=-77,000}

$$\left. \begin{array} { r } { 1 - 14 z = - 350,000 } \\ { 3 y - 7 z = - 77,000 } \end{array} \right.$$

Solve for z, y

$$y = \frac{196001}{6} = 32666\frac{5}{6} \approx 32666.833333333$$

$$z = \frac{350001}{14} = 25000\frac{1}{14} \approx 25000.071428571$$

Solution Steps

Consider the first equation. Subtract 1 from both sides.

$$-14z=-350000-1$$

Subtract 1 from -350000 to get -350001.

$$-14z=-350001$$

Divide both sides by -14.

$$z=\frac{-350001}{-14}$$

Fraction \frac{-350001}{-14} can be simplified to \frac{350001}{14} by removing the negative sign from both the numerator and the denominator.

$$z=\frac{350001}{14}$$

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

$$3y-7\times \frac{350001}{14}=-77000$$

Multiply -7 and \frac{350001}{14} to get -\frac{350001}{2}.

$$3y-\frac{350001}{2}=-77000$$

Add \frac{350001}{2} to both sides.

$$3y=-77000+\frac{350001}{2}$$

Add -77000 and \frac{350001}{2} to get \frac{196001}{2}.

$$3y=\frac{196001}{2}$$

Divide both sides by 3.

$$y=\frac{\frac{196001}{2}}{3}$$

Express \frac{\frac{196001}{2}}{3} as a single fraction.

$$y=\frac{196001}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$y=\frac{196001}{6}$$

The system is now solved.

$$z=\frac{350001}{14} y=\frac{196001}{6}$$