Solve {l}{2x+4y-z+4=13}{3y-7z+6u=4}{4z-4=9}{21u=720}

$$\left\{ \begin{array} { l } { 2 x + 4 y - z + 4 = 13 } \\ { 3 y - 7 z + 6 u = 4 } \\ { 4 z - 4 = 9 } \\ { 21 u = 720 } \end{array} \right.$$

Solve for x, y, z, u

$$x = \frac{21073}{168} = 125\frac{73}{168} \approx 125.43452381$$

$$y = -\frac{5011}{84} = -59\frac{55}{84} \approx -59.654761905$$

$$z = \frac{13}{4} = 3\frac{1}{4} = 3.25$$

$$u = \frac{240}{7} = 34\frac{2}{7} \approx 34.285714286$$

Solution Steps

Consider the third equation. Add 4 to both sides.

$$4z=9+4$$

Add 9 and 4 to get 13.

$$4z=13$$

Divide both sides by 4.

$$z=\frac{13}{4}$$

Consider the fourth equation. Divide both sides by 21.

$$u=\frac{720}{21}$$

Reduce the fraction \frac{720}{21} to lowest terms by extracting and canceling out 3.

$$u=\frac{240}{7}$$

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

$$3y-7\times \frac{13}{4}+6\times \frac{240}{7}=4$$

Multiply -7 and \frac{13}{4} to get -\frac{91}{4}.

$$3y-\frac{91}{4}+6\times \frac{240}{7}=4$$

Multiply 6 and \frac{240}{7} to get \frac{1440}{7}.

$$3y-\frac{91}{4}+\frac{1440}{7}=4$$

Add -\frac{91}{4} and \frac{1440}{7} to get \frac{5123}{28}.

$$3y+\frac{5123}{28}=4$$

Subtract \frac{5123}{28} from both sides.

$$3y=4-\frac{5123}{28}$$

Subtract \frac{5123}{28} from 4 to get -\frac{5011}{28}.

$$3y=-\frac{5011}{28}$$

Divide both sides by 3.

$$y=\frac{-\frac{5011}{28}}{3}$$

Express \frac{-\frac{5011}{28}}{3} as a single fraction.

$$y=\frac{-5011}{28\times 3}$$

Multiply 28 and 3 to get 84.

$$y=\frac{-5011}{84}$$

Fraction \frac{-5011}{84} can be rewritten as -\frac{5011}{84} by extracting the negative sign.

$$y=-\frac{5011}{84}$$

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

$$2x+4\left(-\frac{5011}{84}\right)-\frac{13}{4}+4=13$$

Multiply 4 and -\frac{5011}{84} to get -\frac{5011}{21}.

$$2x-\frac{5011}{21}-\frac{13}{4}+4=13$$

Subtract \frac{13}{4} from -\frac{5011}{21} to get -\frac{20317}{84}.

$$2x-\frac{20317}{84}+4=13$$

Add -\frac{20317}{84} and 4 to get -\frac{19981}{84}.

$$2x-\frac{19981}{84}=13$$

Add \frac{19981}{84} to both sides.

$$2x=13+\frac{19981}{84}$$

Add 13 and \frac{19981}{84} to get \frac{21073}{84}.

$$2x=\frac{21073}{84}$$

Divide both sides by 2.

$$x=\frac{\frac{21073}{84}}{2}$$

Express \frac{\frac{21073}{84}}{2} as a single fraction.

$$x=\frac{21073}{84\times 2}$$

Multiply 84 and 2 to get 168.

$$x=\frac{21073}{168}$$

The system is now solved.

$$x=\frac{21073}{168} y=-\frac{5011}{84} z=\frac{13}{4} u=\frac{240}{7}$$