Solve NP=(x-8,4)quadNM=

$$N P = ( x - 8,4 ) \quad N M =$$

Solve for M

$$\left\{\begin{matrix}M=\frac{P}{x-8,4}\text{, }&x\neq \frac{42}{5}\\M\in \mathrm{R}\text{, }&N=0\text{ or }\left(P=0\text{ and }x=\frac{42}{5}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-8,4 by N.

$$NP=\left(xN-8,4N\right)M$$

Use the distributive property to multiply xN-8,4N by M.

$$NP=xNM-8,4NM$$

Swap sides so that all variable terms are on the left hand side.

$$xNM-8,4NM=NP$$

Combine all terms containing M.

$$\left(xN-8,4N\right)M=NP$$

The equation is in standard form.

$$\left(Nx-\frac{42N}{5}\right)M=NP$$

Divide both sides by xN-8,4N.

$$\frac{\left(Nx-\frac{42N}{5}\right)M}{Nx-\frac{42N}{5}}=\frac{NP}{Nx-\frac{42N}{5}}$$

Dividing by xN-8,4N undoes the multiplication by xN-8,4N.

$$M=\frac{NP}{Nx-\frac{42N}{5}}$$

Divide NP by xN-8,4N.

$$M=\frac{P}{x-8,4}$$

Solve for N

$$\left\{\begin{matrix}\\N=0\text{, }&\text{unconditionally}\\N\in \mathrm{R}\text{, }&P=M\left(x-8,4\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-8,4 by N.

$$NP=\left(xN-8,4N\right)M$$

Use the distributive property to multiply xN-8,4N by M.

$$NP=xNM-8,4NM$$

Subtract xNM from both sides.

$$NP-xNM=-8,4NM$$

Add 8,4NM to both sides.

$$NP-xNM+8,4NM=0$$

Reorder the terms.

$$-MNx+NP+8,4MN=0$$

Combine all terms containing N.

$$\left(-Mx+P+8,4M\right)N=0$$

The equation is in standard form.

$$\left(-Mx+\frac{42M}{5}+P\right)N=0$$

Divide 0 by -Mx+P+8,4M.

$$N=0$$