Solve {l}{x=y/151.497(151-497-60)}{70*10^6=300*151*497*y/2*(350-151.497/3)+(14.6)*900*8*290}

$$\left. \begin{array} { l } { x = \frac { y } { 151.497 } ( 151 - 497 - 60 ) } \\ { 70 \times 10 ^ { 6 } = 300 \times 151 \cdot 497 \times \frac { y } { 2 } \times ( 350 - \frac { 151.497 } { 3 } ) + ( 14.6 ) \times 900 \times 8 \times 290 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{45837632000000}{1459347976892511}\approx -0.031409666$$

$$y=\frac{790304000}{67429954641}\approx 0.01172037$$

Solution Steps

Consider the second equation. Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$420\times 10^{6}=900\times 151\times 497y\left(350-\frac{151.497}{3}\right)+87.6\times 900\times 8\times 290$$

Calculate 10 to the power of 6 and get 1000000.

$$420\times 1000000=900\times 151\times 497y\left(350-\frac{151.497}{3}\right)+87.6\times 900\times 8\times 290$$

Multiply 420 and 1000000 to get 420000000.

$$420000000=900\times 151\times 497y\left(350-\frac{151.497}{3}\right)+87.6\times 900\times 8\times 290$$

Multiply 900 and 151 to get 135900.

$$420000000=135900\times 497y\left(350-\frac{151.497}{3}\right)+87.6\times 900\times 8\times 290$$

Multiply 135900 and 497 to get 67542300.

$$420000000=67542300y\left(350-\frac{151.497}{3}\right)+87.6\times 900\times 8\times 290$$

Expand \frac{151.497}{3} by multiplying both numerator and the denominator by 1000.

$$420000000=67542300y\left(350-\frac{151497}{3000}\right)+87.6\times 900\times 8\times 290$$

Reduce the fraction \frac{151497}{3000} to lowest terms by extracting and canceling out 3.

$$420000000=67542300y\left(350-\frac{50499}{1000}\right)+87.6\times 900\times 8\times 290$$

Subtract \frac{50499}{1000} from 350 to get \frac{299501}{1000}.

$$420000000=67542300y\times \frac{299501}{1000}+87.6\times 900\times 8\times 290$$

Multiply 67542300 and \frac{299501}{1000} to get \frac{202289863923}{10}.

$$420000000=\frac{202289863923}{10}y+87.6\times 900\times 8\times 290$$

Multiply 87.6 and 900 to get 78840.

$$420000000=\frac{202289863923}{10}y+78840\times 8\times 290$$

Multiply 78840 and 8 to get 630720.

$$420000000=\frac{202289863923}{10}y+630720\times 290$$

Multiply 630720 and 290 to get 182908800.

$$420000000=\frac{202289863923}{10}y+182908800$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{202289863923}{10}y+182908800=420000000$$

Subtract 182908800 from both sides.

$$\frac{202289863923}{10}y=420000000-182908800$$

Subtract 182908800 from 420000000 to get 237091200.

$$\frac{202289863923}{10}y=237091200$$

Multiply both sides by \frac{10}{202289863923}, the reciprocal of \frac{202289863923}{10}.

$$y=237091200\times \frac{10}{202289863923}$$

Multiply 237091200 and \frac{10}{202289863923} to get \frac{790304000}{67429954641}.

$$y=\frac{790304000}{67429954641}$$

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

$$x=\frac{\frac{790304000}{67429954641}}{151.497}\left(151-497-60\right)$$

Express \frac{\frac{790304000}{67429954641}}{151.497} as a single fraction.

$$x=\frac{790304000}{67429954641\times 151.497}\left(151-497-60\right)$$

Multiply 67429954641 and 151.497 to get 10215435838247.577.

$$x=\frac{790304000}{10215435838247.577}\left(151-497-60\right)$$

Expand \frac{790304000}{10215435838247.577} by multiplying both numerator and the denominator by 1000.

$$x=\frac{790304000000}{10215435838247577}\left(151-497-60\right)$$

Subtract 497 from 151 to get -346.

$$x=\frac{790304000000}{10215435838247577}\left(-346-60\right)$$

Subtract 60 from -346 to get -406.

$$x=\frac{790304000000}{10215435838247577}\left(-406\right)$$

Multiply \frac{790304000000}{10215435838247577} and -406 to get -\frac{45837632000000}{1459347976892511}.

$$x=-\frac{45837632000000}{1459347976892511}$$

The system is now solved.

$$x=-\frac{45837632000000}{1459347976892511} y=\frac{790304000}{67429954641}$$