Finite Math Examples

2 a - 3 b = - 7

$2 a - 3 b = - 7$ ,

4 a - 6 b = 8

$4 a - 6 b = 8$

Step 1

Solve for

a

$a$ in

2 a - 3 b = - 7

$2 a - 3 b = - 7$ .

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Step 1.1

Add

3 b

$3 b$ to both sides of the equation.

2 a = - 7 + 3 b

$2 a = - 7 + 3 b$

4 a - 6 b = 8

$4 a - 6 b = 8$

Step 1.2

Divide each term in

2 a = - 7 + 3 b

$2 a = - 7 + 3 b$ by

2

$2$ and simplify.

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Step 1.2.1

Divide each term in

2 a = - 7 + 3 b

$2 a = - 7 + 3 b$ by

2

$2$ .

\frac{2 a}{2} = \frac{- 7}{2} + \frac{3 b}{2}

$\frac{2 a}{2} = \frac{- 7}{2} + \frac{3 b}{2}$

4 a - 6 b = 8

$4 a - 6 b = 8$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of

2

$2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{- 7}{2} + \frac{3 b}{2}$

$4 a - 6 b = 8$

Step 1.2.2.1.2

Divide

$a$ by

$1$ .

$a = \frac{- 7}{2} + \frac{3 b}{2}$

$4 a - 6 b = 8$

$a = \frac{- 7}{2} + \frac{3 b}{2}$

$4 a - 6 b = 8$

$a = \frac{- 7}{2} + \frac{3 b}{2}$

$4 a - 6 b = 8$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

$a = - \frac{7}{2} + \frac{3 b}{2}$

$4 a - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

$4 a - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

$4 a - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

$4 a - 6 b = 8$

Step 2

Replace all occurrences of

$a$ with

$- \frac{7}{2} + \frac{3 b}{2}$ in each equation.

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Step 2.1

Replace all occurrences of

$a$ in

$4 a - 6 b = 8$ with

$- \frac{7}{2} + \frac{3 b}{2}$ .

$4 (- \frac{7}{2} + \frac{3 b}{2}) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify

$4 (- \frac{7}{2} + \frac{3 b}{2}) - 6 b$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$4 (- \frac{7}{2}) + 4 (\frac{3 b}{2}) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2.1.1.2

Cancel the common factor of

$2$ .

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Step 2.2.1.1.2.1

Move the leading negative in

$- \frac{7}{2}$ into the numerator.

$4 (\frac{- 7}{2}) + 4 (\frac{3 b}{2}) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2.1.1.2.2

Factor

$2$ out of

$4$ .

$2 (2) (\frac{- 7}{2}) + 4 (\frac{3 b}{2}) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2.1.1.2.3

Cancel the common factor.

$2 \cdot (2 (\frac{- 7}{2})) + 4 (\frac{3 b}{2}) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2.1.1.2.4

Rewrite the expression.

$2 \cdot - 7 + 4 (\frac{3 b}{2}) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

$2 \cdot - 7 + 4 (\frac{3 b}{2}) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2.1.1.3

Multiply

$2$ by

$- 7$ .

$- 14 + 4 (\frac{3 b}{2}) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2.1.1.4

Cancel the common factor of

$2$ .

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Step 2.2.1.1.4.1

Factor

$2$ out of

$4$ .

$- 14 + 2 (2) (\frac{3 b}{2}) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2.1.1.4.2

Cancel the common factor.

$- 14 + 2 \cdot (2 (\frac{3 b}{2})) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2.1.1.4.3

Rewrite the expression.

$- 14 + 2 (3 b) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

$- 14 + 2 (3 b) - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2.1.1.5

Multiply

$3$ by

$2$ .

$- 14 + 6 b - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

$- 14 + 6 b - 6 b = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2.1.2

Combine the opposite terms in

$- 14 + 6 b - 6 b$ .

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Step 2.2.1.2.1

Subtract

$6 b$ from

$6 b$ .

$- 14 + 0 = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 2.2.1.2.2

Add

$- 14$ and

$0$ .

$- 14 = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

$- 14 = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

$- 14 = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

$- 14 = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

$- 14 = 8$

$a = - \frac{7}{2} + \frac{3 b}{2}$

Step 3

Since

$- 14 = 8$ is not true, there is no solution.

No solution