Solve frac{14(a_{1}+a_{1}+3a_{2})}{2}-frac{11(a_{1}+a_{1}+ba_{2})}{2}=14

$$\frac { 14 ( a _ { 1 } + a _ { 1 } + 3 a _ { 2 } ) } { 2 } - \frac { 11 ( a _ { 1 } + a _ { 1 } + b a _ { 2 } ) } { 2 } = 14$$

Solve for a_2 (complex solution)

$$\left\{\begin{matrix}a_{2}=-\frac{2\left(3a_{1}-14\right)}{42-11b}\text{, }&b\neq \frac{42}{11}\\a_{2}\in \mathrm{C}\text{, }&a_{1}=\frac{14}{3}\text{ and }b=\frac{42}{11}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$14\left(a_{1}+a_{1}+3a_{2}\right)-11\left(a_{1}+a_{1}+ba_{2}\right)=28$$

Combine a_{1} and a_{1} to get 2a_{1}.

$$14\left(2a_{1}+3a_{2}\right)-11\left(a_{1}+a_{1}+ba_{2}\right)=28$$

Use the distributive property to multiply 14 by 2a_{1}+3a_{2}.

$$28a_{1}+42a_{2}-11\left(a_{1}+a_{1}+ba_{2}\right)=28$$

Combine a_{1} and a_{1} to get 2a_{1}.

$$28a_{1}+42a_{2}-11\left(2a_{1}+ba_{2}\right)=28$$

Use the distributive property to multiply -11 by 2a_{1}+ba_{2}.

$$28a_{1}+42a_{2}-22a_{1}-11ba_{2}=28$$

Combine 28a_{1} and -22a_{1} to get 6a_{1}.

$$6a_{1}+42a_{2}-11ba_{2}=28$$

Subtract 6a_{1} from both sides.

$$42a_{2}-11ba_{2}=28-6a_{1}$$

Combine all terms containing a_{2}.

$$\left(42-11b\right)a_{2}=28-6a_{1}$$

Divide both sides by 42-11b.

$$\frac{\left(42-11b\right)a_{2}}{42-11b}=\frac{28-6a_{1}}{42-11b}$$

Dividing by 42-11b undoes the multiplication by 42-11b.

$$a_{2}=\frac{28-6a_{1}}{42-11b}$$

Divide 28-6a_{1} by 42-11b.

$$a_{2}=\frac{2\left(14-3a_{1}\right)}{42-11b}$$

Solve for a_1

$$a_{1}=\frac{11a_{2}b}{6}-7a_{2}+\frac{14}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$14\left(a_{1}+a_{1}+3a_{2}\right)-11\left(a_{1}+a_{1}+ba_{2}\right)=28$$

Combine a_{1} and a_{1} to get 2a_{1}.

$$14\left(2a_{1}+3a_{2}\right)-11\left(a_{1}+a_{1}+ba_{2}\right)=28$$

Use the distributive property to multiply 14 by 2a_{1}+3a_{2}.

$$28a_{1}+42a_{2}-11\left(a_{1}+a_{1}+ba_{2}\right)=28$$

Combine a_{1} and a_{1} to get 2a_{1}.

$$28a_{1}+42a_{2}-11\left(2a_{1}+ba_{2}\right)=28$$

Use the distributive property to multiply -11 by 2a_{1}+ba_{2}.

$$28a_{1}+42a_{2}-22a_{1}-11ba_{2}=28$$

Combine 28a_{1} and -22a_{1} to get 6a_{1}.

$$6a_{1}+42a_{2}-11ba_{2}=28$$

Subtract 42a_{2} from both sides.

$$6a_{1}-11ba_{2}=28-42a_{2}$$

Add 11ba_{2} to both sides.

$$6a_{1}=28-42a_{2}+11ba_{2}$$

The equation is in standard form.

$$6a_{1}=11a_{2}b-42a_{2}+28$$

Divide both sides by 6.

$$\frac{6a_{1}}{6}=\frac{11a_{2}b-42a_{2}+28}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$a_{1}=\frac{11a_{2}b-42a_{2}+28}{6}$$

Divide 28-42a_{2}+11ba_{2} by 6.

$$a_{1}=\frac{11a_{2}b}{6}-7a_{2}+\frac{14}{3}$$

Solve for a_2

$$\left\{\begin{matrix}a_{2}=-\frac{2\left(3a_{1}-14\right)}{42-11b}\text{, }&b\neq \frac{42}{11}\\a_{2}\in \mathrm{R}\text{, }&a_{1}=\frac{14}{3}\text{ and }b=\frac{42}{11}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$14\left(a_{1}+a_{1}+3a_{2}\right)-11\left(a_{1}+a_{1}+ba_{2}\right)=28$$

Combine a_{1} and a_{1} to get 2a_{1}.

$$14\left(2a_{1}+3a_{2}\right)-11\left(a_{1}+a_{1}+ba_{2}\right)=28$$

Use the distributive property to multiply 14 by 2a_{1}+3a_{2}.

$$28a_{1}+42a_{2}-11\left(a_{1}+a_{1}+ba_{2}\right)=28$$

Combine a_{1} and a_{1} to get 2a_{1}.

$$28a_{1}+42a_{2}-11\left(2a_{1}+ba_{2}\right)=28$$

Use the distributive property to multiply -11 by 2a_{1}+ba_{2}.

$$28a_{1}+42a_{2}-22a_{1}-11ba_{2}=28$$

Combine 28a_{1} and -22a_{1} to get 6a_{1}.

$$6a_{1}+42a_{2}-11ba_{2}=28$$

Subtract 6a_{1} from both sides.

$$42a_{2}-11ba_{2}=28-6a_{1}$$

Combine all terms containing a_{2}.

$$\left(42-11b\right)a_{2}=28-6a_{1}$$

Divide both sides by 42-11b.

$$\frac{\left(42-11b\right)a_{2}}{42-11b}=\frac{28-6a_{1}}{42-11b}$$

Dividing by 42-11b undoes the multiplication by 42-11b.

$$a_{2}=\frac{28-6a_{1}}{42-11b}$$

Divide 28-6a_{1} by 42-11b.

$$a_{2}=\frac{2\left(14-3a_{1}\right)}{42-11b}$$