Solve (3x+2y)n/xn=97^circ/100

$$\frac { ( 3 x + 2 y ) n } { x n } = \frac { 97 ^ { \circ } } { 100 }$$

Solve for n

$$n\neq 0$$

$$y=-\frac{203x}{200}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100nx, the least common multiple of xn,100.

$$100\left(3x+2y\right)n=97nx$$

Use the distributive property to multiply 100 by 3x+2y.

$$\left(300x+200y\right)n=97nx$$

Use the distributive property to multiply 300x+200y by n.

$$300xn+200yn=97nx$$

Subtract 97nx from both sides.

$$300xn+200yn-97nx=0$$

Combine 300xn and -97nx to get 203xn.

$$203xn+200yn=0$$

Combine all terms containing n.

$$\left(203x+200y\right)n=0$$

Divide 0 by 203x+200y.

$$n=0$$

Variable n cannot be equal to 0.

$$n\in \emptyset$$

Solve for x

$$x=-\frac{200y}{203}$$

$$y\neq 0\text{ and }n\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100nx, the least common multiple of xn,100.

$$100\left(3x+2y\right)n=97nx$$

Use the distributive property to multiply 100 by 3x+2y.

$$\left(300x+200y\right)n=97nx$$

Use the distributive property to multiply 300x+200y by n.

$$300xn+200yn=97nx$$

Subtract 97nx from both sides.

$$300xn+200yn-97nx=0$$

Combine 300xn and -97nx to get 203xn.

$$203xn+200yn=0$$

Subtract 200yn from both sides. Anything subtracted from zero gives its negation.

$$203xn=-200yn$$

The equation is in standard form.

$$203nx=-200ny$$

Divide both sides by 203n.

$$\frac{203nx}{203n}=-\frac{200ny}{203n}$$

Dividing by 203n undoes the multiplication by 203n.

$$x=-\frac{200ny}{203n}$$

Divide -200yn by 203n.

$$x=-\frac{200y}{203}$$

Variable x cannot be equal to 0.

$$x=-\frac{200y}{203}\text{, }x\neq 0$$