Solve {l}{h^6y+10^6y=1}{x=y}

$$\left. \begin{array} { l } { h ^ { 6 } y + 10 ^ { 6 } y = 1 } \\ { x = y } \end{array} \right.$$

Solve for x, y

$$x=\frac{1}{h^{6}+1000000}$$

$$y=\frac{1}{h^{6}+1000000}$$

Steps Using Substitution

Consider the first equation. Calculate 10 to the power of 6 and get 1000000.

$$h^{6}y+1000000y=1$$

Combine all terms containing x,y.

$$\left(h^{6}+1000000\right)y=1$$

Consider the second equation. Subtract y from both sides.

$$x-y=0$$

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.

$$\left(h^{6}+1000000\right)y=1,-y+x=0$$

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

$$\left(h^{6}+1000000\right)y=1$$

Divide both sides by h^{6}+1000000.

$$y=\frac{1}{\left(h^{2}+100\right)\left(h^{4}-100h^{2}+10000\right)}$$

Substitute \frac{1}{\left(h^{2}+100\right)\left(h^{4}-100h^{2}+10000\right)} for y in the other equation, -y+x=0.

$$-\frac{1}{\left(h^{2}+100\right)\left(h^{4}-100h^{2}+10000\right)}+x=0$$

Add \frac{1}{\left(h^{2}+100\right)\left(h^{4}-100h^{2}+10000\right)} to both sides of the equation.

$$x=\frac{1}{\left(h^{2}+100\right)\left(h^{4}-100h^{2}+10000\right)}$$

The system is now solved.

$$y=\frac{1}{\left(h^{2}+100\right)\left(h^{4}-100h^{2}+10000\right)},x=\frac{1}{\left(h^{2}+100\right)\left(h^{4}-100h^{2}+10000\right)}$$