Solve {l}{W=6.67*10^-31X}{W=4.7/1.6*10^-19}

$$\left\{ \begin{array} { l } { W = 6.67 \times 10 ^ { - 31 } X } \\ { W = \frac { 4.7 } { 1.6 \times 10 ^ { - 19 } } } \end{array} \right.$$

Solve for W, X

$$W=29375000000000000000$$

$$X=\frac{29375000000000000000000000000000000000000000000000000}{667}\approx 4.404047976 \cdot 10^{49}$$

Steps Using Substitution

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

$$W=\frac{4.7}{1.6\times \left(\frac{1}{10000000000000000000}\right)}$$

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

$$W=6.67\times \left(\frac{1}{10000000000000000000000000000000}\right)X$$

Subtract 6.67\times \left(\frac{1}{10000000000000000000000000000000}\right)X from both sides.

$$W-6.67\times \left(\frac{1}{10000000000000000000000000000000}\right)X=0$$

Reorder the terms.

$$-X\left(6.67\times \left(\frac{1}{10000000000000000000000000000000}\right)\right)+W=0$$

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.

$$W=\frac{4.7}{1.6\times \left(\frac{1}{10000000000000000000}\right)},W+\left(-6.67\times \left(\frac{1}{10000000000000000000000000000000}\right)\right)X=0$$

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

$$W=\frac{4.7}{1.6\times \left(\frac{1}{10000000000000000000}\right)}$$

Divide both sides by 1.

$$W=29375000000000000000$$

Substitute 29375000000000000000 for W in the other equation, W+\left(-6.67\times \left(\frac{1}{10000000000000000000000000000000}\right)\right)X=0.

$$29375000000000000000+\left(-6.67\times \left(\frac{1}{10000000000000000000000000000000}\right)\right)X=0$$

Subtract 29375000000000000000 from both sides of the equation.

$$-\frac{667}{1000000000000000000000000000000000}X=-29375000000000000000$$

Divide both sides of the equation by -\frac{667}{1000000000000000000000000000000000}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$X=\frac{29375000000000000000000000000000000000000000000000000}{667}$$

The system is now solved.

$$W=29375000000000000000,X=\frac{29375000000000000000000000000000000000000000000000000}{667}$$