Solve {l}{3*10^7m=0.06}{y=1/21.6*10^-19*200/9*10^-31*0.02m}

$$\left\{ \begin{array} { l } { 3 \times 10 ^ { 7 } m = 0.06 } \\ { y = \frac { 1 } { 2 } \frac { 1.6 \times 10 ^ { - 19 } \times 200 } { 9 \times 10 ^ { - 31 } \times 0.02 } m } \end{array} \right.$$

Solve for m, y

$$y = \frac{16000000}{9} = 1777777\frac{7}{9} \approx 1777777.777777778$$

$$m=0.000000002$$

Steps Using Substitution

Consider the first equation. Calculate 10 to the power of 7 and get 10000000.

$$3\times 10000000m=0.06$$

Consider the second equation. Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$y=\frac{1}{2}\times \frac{1.6\times \left(\frac{1}{10000000000000000000}\right)\times 200}{9\times 10^{-31}\times 0.02}m$$

Calculate 10 to the power of -31 and get \frac{1}{10000000000000000000000000000000}.

$$y=\frac{1}{2}\times \frac{1.6\times \left(\frac{1}{10000000000000000000}\right)\times 200}{9\times \left(\frac{1}{10000000000000000000000000000000}\right)\times 0.02}m$$

Subtract \frac{1}{2}\times \frac{1.6\times \left(\frac{1}{10000000000000000000}\right)\times 200}{9\times \left(\frac{1}{10000000000000000000000000000000}\right)\times 0.02}m from both sides.

$$y-\frac{1}{2}\times \frac{1.6\times \left(\frac{1}{10000000000000000000}\right)\times 200}{9\times \left(\frac{1}{10000000000000000000000000000000}\right)\times 0.02}m=0$$

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.

$$30000000m=0.06,-\frac{8000000000000000}{9}m+y=0$$

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

$$30000000m=0.06$$

Divide both sides by 30000000.

$$m=0.000000002$$

Substitute 0.000000002 for m in the other equation, -\frac{8000000000000000}{9}m+y=0.

$$-\frac{8000000000000000}{9}\times 0.000000002+y=0$$

Multiply -\frac{8000000000000000}{9} times 0.000000002 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{16000000}{9}+y=0$$

Add \frac{16000000}{9} to both sides of the equation.

$$y=\frac{16000000}{9}$$

The system is now solved.

$$m=0.000000002,y=\frac{16000000}{9}$$