Solve {l}{0.9x-y=0}{x-ytan6^circ=11760/cos6^circ}

$$\left. \begin{array} { l } { 0.9 x - y = 0 } \\ { x - y \tan 6 ^ { \circ } = \frac { 11760 } { \cos 6 ^ { \circ } } } \end{array} \right.$$

Solve for x, y

$$x=\frac{5255211763283823y_{0}}{50000000000000000}+\frac{5600000000000000000}{473581854937273}$$

$$y=\frac{47296905869554407y_{0}}{500000000000000000}+\frac{5040000000000000000}{473581854937273}$$

Steps Using Substitution

Evaluate trigonometric functions in the problem

$$\left. \begin{array} { l } { 0.9 x - y = 0 }\\ { x - y 0.10510423526567646 = \frac{11760}{0.9945218953682733} } \end{array} \right.$$

Consider the second equation. Expand \frac{11760}{0.9945218953682733} by multiplying both numerator and the denominator by 10000000000000000.

$$x-y_{0}\times 0.10510423526567646=\frac{117600000000000000000}{9945218953682733}$$

Reduce the fraction \frac{117600000000000000000}{9945218953682733} to lowest terms by extracting and canceling out 21.

$$x-y_{0}\times 0.10510423526567646=\frac{5600000000000000000}{473581854937273}$$

Add y_{0}\times 0.10510423526567646 to both sides.

$$x=\frac{5600000000000000000}{473581854937273}+y_{0}\times 0.10510423526567646$$

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.

$$x=\frac{5255211763283823y_{0}}{50000000000000000}+\frac{5600000000000000000}{473581854937273},0.9x-y=0$$

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

$$x=\frac{5255211763283823y_{0}}{50000000000000000}+\frac{5600000000000000000}{473581854937273}$$

Substitute \frac{5255211763283823y_{0}}{50000000000000000}+\frac{5600000000000000000}{473581854937273} for x in the other equation, 0.9x-y=0.

$$0.9\left(\frac{5255211763283823y_{0}}{50000000000000000}+\frac{5600000000000000000}{473581854937273}\right)-y=0$$

Multiply 0.9 times \frac{5255211763283823y_{0}}{50000000000000000}+\frac{5600000000000000000}{473581854937273}.

$$\frac{47296905869554407y_{0}}{500000000000000000}+\frac{5040000000000000000}{473581854937273}-y=0$$

Subtract \frac{47296905869554407y_{0}}{500000000000000000}+\frac{5040000000000000000}{473581854937273} from both sides of the equation.

$$-y=-\frac{47296905869554407y_{0}}{500000000000000000}-\frac{5040000000000000000}{473581854937273}$$

Divide both sides by -1.

$$y=\frac{47296905869554407y_{0}}{500000000000000000}+\frac{5040000000000000000}{473581854937273}$$

The system is now solved.

$$x=\frac{5255211763283823y_{0}}{50000000000000000}+\frac{5600000000000000000}{473581854937273},y=\frac{47296905869554407y_{0}}{500000000000000000}+\frac{5040000000000000000}{473581854937273}$$