Solve {l}{f(x)=6x}{g(y)=7x}

$$\left. \begin{array} { l } { f ( x ) = 6 x } \\ { g ( y ) = 7 x } \end{array} \right.$$

Solve for x, y (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }y=0\text{, }&\text{unconditionally}\\x=\frac{gy}{7}\text{, }y\in \mathrm{C}\text{, }&f=6\text{ or }g=0\end{matrix}\right.$$

Steps Using Substitution

Consider the first equation. Subtract 6x from both sides.

$$fx-6x=0$$

Combine all terms containing x,y.

$$\left(f-6\right)x=0$$

Consider the second equation. Subtract 7x from both sides.

$$gy-7x=0$$

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.

$$\left(f-6\right)x=0,-7x+gy=0$$

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.

$$\left(f-6\right)x=0$$

Divide both sides by -6+f.

$$x=0$$

Substitute 0 for x in the other equation, -7x+gy=0.

$$gy=0$$

Divide both sides by g.

$$y=0$$

The system is now solved.

$$x=0,y=0$$

Solve for x, y

$$\left\{\begin{matrix}\\x=0\text{, }y=0\text{, }&\text{unconditionally}\\x=\frac{gy}{7}\text{, }y\in \mathrm{R}\text{, }&f=6\text{ or }g=0\end{matrix}\right.$$

Steps Using Substitution

Consider the first equation. Subtract 6x from both sides.

$$fx-6x=0$$

Combine all terms containing x,y.

$$\left(f-6\right)x=0$$

Consider the second equation. Subtract 7x from both sides.

$$gy-7x=0$$

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.

$$\left(f-6\right)x=0,-7x+gy=0$$

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.

$$\left(f-6\right)x=0$$

Divide both sides by -6+f.

$$x=0$$

Substitute 0 for x in the other equation, -7x+gy=0.

$$gy=0$$

Divide both sides by g.

$$y=0$$

The system is now solved.

$$x=0,y=0$$