Solve 5varphi+2=17quadtext{(a)}3m-14=

$$5 \varphi + 2 = 17 \quad \text { (a) } 3 m - 14 =$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{5\phi +16}{51m}\text{, }&m\neq 0\\a\in \mathrm{C}\text{, }&\phi =-\frac{16}{5}\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 17 and 3 to get 51.

$$5\phi +2=51am-14$$

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

$$51am-14=5\phi +2$$

Add 14 to both sides.

$$51am=5\phi +2+14$$

Add 2 and 14 to get 16.

$$51am=5\phi +16$$

The equation is in standard form.

$$51ma=5\phi +16$$

Divide both sides by 51m.

$$\frac{51ma}{51m}=\frac{5\phi +16}{51m}$$

Dividing by 51m undoes the multiplication by 51m.

$$a=\frac{5\phi +16}{51m}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{5\phi +16}{51a}\text{, }&a\neq 0\\m\in \mathrm{C}\text{, }&\phi =-\frac{16}{5}\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 17 and 3 to get 51.

$$5\phi +2=51am-14$$

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

$$51am-14=5\phi +2$$

Add 14 to both sides.

$$51am=5\phi +2+14$$

Add 2 and 14 to get 16.

$$51am=5\phi +16$$

Divide both sides by 51a.

$$\frac{51am}{51a}=\frac{5\phi +16}{51a}$$

Dividing by 51a undoes the multiplication by 51a.

$$m=\frac{5\phi +16}{51a}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{5\phi +16}{51m}\text{, }&m\neq 0\\a\in \mathrm{R}\text{, }&\phi =-\frac{16}{5}\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 17 and 3 to get 51.

$$5\phi +2=51am-14$$

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

$$51am-14=5\phi +2$$

Add 14 to both sides.

$$51am=5\phi +2+14$$

Add 2 and 14 to get 16.

$$51am=5\phi +16$$

The equation is in standard form.

$$51ma=5\phi +16$$

Divide both sides by 51m.

$$\frac{51ma}{51m}=\frac{5\phi +16}{51m}$$

Dividing by 51m undoes the multiplication by 51m.

$$a=\frac{5\phi +16}{51m}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{5\phi +16}{51a}\text{, }&a\neq 0\\m\in \mathrm{R}\text{, }&\phi =-\frac{16}{5}\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 17 and 3 to get 51.

$$5\phi +2=51am-14$$

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

$$51am-14=5\phi +2$$

Add 14 to both sides.

$$51am=5\phi +2+14$$

Add 2 and 14 to get 16.

$$51am=5\phi +16$$

Divide both sides by 51a.

$$\frac{51am}{51a}=\frac{5\phi +16}{51a}$$

Dividing by 51a undoes the multiplication by 51a.

$$m=\frac{5\phi +16}{51a}$$