Solve =4a_{1}+bd=10quad4-2/14

$$= 4 a _ { 1 } + b d = 10 \quad 4 - \frac { 2 } { 14 }$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{28a_{1}-279}{7d}\text{, }&d\neq 0\\b\in \mathrm{C}\text{, }&a_{1}=\frac{279}{28}\text{ and }d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 10 and 4 to get 40.

$$4a_{1}+bd=40-\frac{2}{14}$$

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$4a_{1}+bd=40-\frac{1}{7}$$

Subtract \frac{1}{7} from 40 to get \frac{279}{7}.

$$4a_{1}+bd=\frac{279}{7}$$

Subtract 4a_{1} from both sides.

$$bd=\frac{279}{7}-4a_{1}$$

The equation is in standard form.

$$db=\frac{279}{7}-4a_{1}$$

Divide both sides by d.

$$\frac{db}{d}=\frac{\frac{279}{7}-4a_{1}}{d}$$

Dividing by d undoes the multiplication by d.

$$b=\frac{\frac{279}{7}-4a_{1}}{d}$$

Divide \frac{279}{7}-4a_{1} by d.

$$b=\frac{279-28a_{1}}{7d}$$

Solve for a_1

$$a_{1}=-\frac{bd}{4}+\frac{279}{28}$$

Steps for Solving Linear Equation

Multiply 10 and 4 to get 40.

$$4a_{1}+bd=40-\frac{2}{14}$$

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$4a_{1}+bd=40-\frac{1}{7}$$

Subtract \frac{1}{7} from 40 to get \frac{279}{7}.

$$4a_{1}+bd=\frac{279}{7}$$

Subtract bd from both sides.

$$4a_{1}=\frac{279}{7}-bd$$

Divide both sides by 4.

$$\frac{4a_{1}}{4}=\frac{\frac{279}{7}-bd}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$a_{1}=\frac{\frac{279}{7}-bd}{4}$$

Divide \frac{279}{7}-bd by 4.

$$a_{1}=-\frac{bd}{4}+\frac{279}{28}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{28a_{1}-279}{7d}\text{, }&d\neq 0\\b\in \mathrm{R}\text{, }&a_{1}=\frac{279}{28}\text{ and }d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 10 and 4 to get 40.

$$4a_{1}+bd=40-\frac{2}{14}$$

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$4a_{1}+bd=40-\frac{1}{7}$$

Subtract \frac{1}{7} from 40 to get \frac{279}{7}.

$$4a_{1}+bd=\frac{279}{7}$$

Subtract 4a_{1} from both sides.

$$bd=\frac{279}{7}-4a_{1}$$

The equation is in standard form.

$$db=\frac{279}{7}-4a_{1}$$

Divide both sides by d.

$$\frac{db}{d}=\frac{\frac{279}{7}-4a_{1}}{d}$$

Dividing by d undoes the multiplication by d.

$$b=\frac{\frac{279}{7}-4a_{1}}{d}$$

Divide \frac{279}{7}-4a_{1} by d.

$$b=\frac{279-28a_{1}}{7d}$$