Solve R=10Ni+54Nj

$$R = 10 N i + 54 N j$$

Solve for N

$$\left\{\begin{matrix}N=\frac{R}{2\left(27j+5i\right)}\text{, }&j\neq -\frac{5}{27}i\\N\in \mathrm{C}\text{, }&R=0\text{ and }j=-\frac{5}{27}i\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 10 and i to get 10i.

$$R=10iN+54Nj$$

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

$$10iN+54Nj=R$$

Combine all terms containing N.

$$\left(10i+54j\right)N=R$$

The equation is in standard form.

$$\left(54j+10i\right)N=R$$

Divide both sides by 10i+54j.

$$\frac{\left(54j+10i\right)N}{54j+10i}=\frac{R}{54j+10i}$$

Dividing by 10i+54j undoes the multiplication by 10i+54j.

$$N=\frac{R}{54j+10i}$$

Divide R by 10i+54j.

$$N=\frac{R}{2\left(27j+5i\right)}$$

Solve for R

$$R=2N\left(27j+5i\right)$$

Solution Steps

Multiply 10 and i to get 10i.

$$R=10iN+54Nj$$