Solve 7x+ay=42

$$7 x + a y = 42$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{7\left(x-6\right)}{y}\text{, }&y\neq 0\\a\in \mathrm{C}\text{, }&x=6\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 7x from both sides.

$$ay=42-7x$$

The equation is in standard form.

$$ya=42-7x$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{42-7x}{y}$$

Dividing by y undoes the multiplication by y.

$$a=\frac{42-7x}{y}$$

Divide 42-7x by y.

$$a=\frac{7\left(6-x\right)}{y}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{7\left(x-6\right)}{y}\text{, }&y\neq 0\\a\in \mathrm{R}\text{, }&x=6\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 7x from both sides.

$$ay=42-7x$$

The equation is in standard form.

$$ya=42-7x$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{42-7x}{y}$$

Dividing by y undoes the multiplication by y.

$$a=\frac{42-7x}{y}$$

Divide 42-7x by y.

$$a=\frac{7\left(6-x\right)}{y}$$

Solve for x

$$x=-\frac{ay}{7}+6$$

Steps for Solving Linear Equation

Subtract ay from both sides.

$$7x=42-ay$$

Divide both sides by 7.

$$\frac{7x}{7}=\frac{42-ay}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x=\frac{42-ay}{7}$$

Divide 42-ay by 7.

$$x=-\frac{ay}{7}+6$$