Solve a_{5}=3a_{3}+4a_{1}

$$a _ { 5 } = 3 a _ { 3 } + 4 a _ { 1 }$$

Solve for a_1

$$a_{1}=\frac{a_{5}-3a_{3}}{4}$$

Steps for Solving Linear Equation

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

$$3a_{3}+4a_{1}=a_{5}$$

Subtract 3a_{3} from both sides.

$$4a_{1}=a_{5}-3a_{3}$$

Divide both sides by 4.

$$\frac{4a_{1}}{4}=\frac{a_{5}-3a_{3}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$a_{1}=\frac{a_{5}-3a_{3}}{4}$$

Solve for a_3

$$a_{3}=\frac{a_{5}-4a_{1}}{3}$$

Steps for Solving Linear Equation

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

$$3a_{3}+4a_{1}=a_{5}$$

Subtract 4a_{1} from both sides.

$$3a_{3}=a_{5}-4a_{1}$$

Divide both sides by 3.

$$\frac{3a_{3}}{3}=\frac{a_{5}-4a_{1}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$a_{3}=\frac{a_{5}-4a_{1}}{3}$$