Solve {l}{2/sqrt{29}L-5/sqrt{29}D=0}{5/sqrt{29}L-02/sqrt{29}0-1500*9.81=0}

$$\left. \begin{array} { l } { \frac { 2 } { \sqrt { 29 } } L - \frac { 5 } { \sqrt { 29 } } D = 0 } \\ { \frac { 5 } { \sqrt { 29 } } L - \frac { 02 } { \sqrt { 29 } } 0 - 1500 \times 9.81 = 0 } \end{array} \right.$$

Solve for L, D

$$L=2943\sqrt{29}\approx 15848.540027397$$

$$D = \frac{5886 \sqrt{29}}{5} \approx 6339.416010959$$

Steps Using Substitution

Consider the second equation. Rationalize the denominator of \frac{5}{\sqrt{29}} by multiplying numerator and denominator by \sqrt{29}.

$$\frac{5\sqrt{29}}{\left(\sqrt{29}\right)^{2}}L-0\times \frac{0\times 2}{\sqrt{29}}-1500\times 9.81=0$$

The square of \sqrt{29} is 29.

$$\frac{5\sqrt{29}}{29}L-0\times \frac{0\times 2}{\sqrt{29}}-1500\times 9.81=0$$

Express \frac{5\sqrt{29}}{29}L as a single fraction.

$$\frac{5\sqrt{29}L}{29}-0\times \frac{0\times 2}{\sqrt{29}}-1500\times 9.81=0$$

Multiply 0 and 2 to get 0.

$$\frac{5\sqrt{29}L}{29}-0\times \frac{0}{\sqrt{29}}-1500\times 9.81=0$$

Rationalize the denominator of \frac{0}{\sqrt{29}} by multiplying numerator and denominator by \sqrt{29}.

$$\frac{5\sqrt{29}L}{29}-0\times \frac{0\sqrt{29}}{\left(\sqrt{29}\right)^{2}}-1500\times 9.81=0$$

The square of \sqrt{29} is 29.

$$\frac{5\sqrt{29}L}{29}-0\times \frac{0\sqrt{29}}{29}-1500\times 9.81=0$$

Anything times zero gives zero.

$$\frac{5\sqrt{29}L}{29}-0\times \frac{0}{29}-1500\times 9.81=0$$

Zero divided by any non-zero number gives zero.

$$\frac{5\sqrt{29}L}{29}-0\times 0-1500\times 9.81=0$$

Multiply 0 and 0 to get 0.

$$\frac{5\sqrt{29}L}{29}-0-1500\times 9.81=0$$

Multiply 1500 and 9.81 to get 14715.

$$\frac{5\sqrt{29}L}{29}-0-14715=0$$

Add 14715 to both sides. Anything plus zero gives itself.

$$\frac{5\sqrt{29}L}{29}-0=14715$$

Add 0 to both sides.

$$\frac{5\sqrt{29}L}{29}=14715+0$$

Add 14715 and 0 to get 14715.

$$\frac{5\sqrt{29}L}{29}=14715$$

Multiply both sides by 29.

$$5\sqrt{29}L=14715\times 29$$

Multiply 14715 and 29 to get 426735.

$$5\sqrt{29}L=426735$$

Consider the first equation. Rationalize the denominator of \frac{2}{\sqrt{29}} by multiplying numerator and denominator by \sqrt{29}.

$$\frac{2\sqrt{29}}{\left(\sqrt{29}\right)^{2}}L-\frac{5}{\sqrt{29}}D=0$$

The square of \sqrt{29} is 29.

$$\frac{2\sqrt{29}}{29}L-\frac{5}{\sqrt{29}}D=0$$

Express \frac{2\sqrt{29}}{29}L as a single fraction.

$$\frac{2\sqrt{29}L}{29}-\frac{5}{\sqrt{29}}D=0$$

Rationalize the denominator of \frac{5}{\sqrt{29}} by multiplying numerator and denominator by \sqrt{29}.

$$\frac{2\sqrt{29}L}{29}-\frac{5\sqrt{29}}{\left(\sqrt{29}\right)^{2}}D=0$$

The square of \sqrt{29} is 29.

$$\frac{2\sqrt{29}L}{29}-\frac{5\sqrt{29}}{29}D=0$$

Express \frac{5\sqrt{29}}{29}D as a single fraction.

$$\frac{2\sqrt{29}L}{29}-\frac{5\sqrt{29}D}{29}=0$$

Since \frac{2\sqrt{29}L}{29} and \frac{5\sqrt{29}D}{29} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\sqrt{29}L-5\sqrt{29}D}{29}=0$$

Multiply both sides by 29. Anything times zero gives zero.

$$2\sqrt{29}L-5\sqrt{29}D=0$$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$5\sqrt{29}L=426735,2\sqrt{29}L+\left(-5\sqrt{29}\right)D=0$$

Pick one of the two equations which is more simple to solve for L by isolating L on the left hand side of the equal sign.

$$5\sqrt{29}L=426735$$

Divide both sides by 5\sqrt{29}.

$$L=2943\sqrt{29}$$

Substitute 2943\sqrt{29} for L in the other equation, 2\sqrt{29}L+\left(-5\sqrt{29}\right)D=0.

$$2\sqrt{29}\times 2943\sqrt{29}+\left(-5\sqrt{29}\right)D=0$$

Multiply 2\sqrt{29} times 2943\sqrt{29}.

$$170694+\left(-5\sqrt{29}\right)D=0$$

Subtract 170694 from both sides of the equation.

$$\left(-5\sqrt{29}\right)D=-170694$$

Divide both sides by -5\sqrt{29}.

$$D=\frac{5886\sqrt{29}}{5}$$

The system is now solved.

$$L=2943\sqrt{29},D=\frac{5886\sqrt{29}}{5}$$