Finite Math Examples

$2 x = y - 7$ , $4 x - 2 y = 14$

Step 1

Divide each term in $2 x = y - 7$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 x = y - 7$ by $2$ .

$\frac{2 x}{2} = \frac{y}{2} + \frac{- 7}{2}$

$4 x - 2 y = 14$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{y}{2} + \frac{- 7}{2}$

$4 x - 2 y = 14$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{y}{2} + \frac{- 7}{2}$

$4 x - 2 y = 14$

$x = \frac{y}{2} + \frac{- 7}{2}$

$4 x - 2 y = 14$

$x = \frac{y}{2} + \frac{- 7}{2}$

$4 x - 2 y = 14$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative in front of the fraction.

$x = \frac{y}{2} - \frac{7}{2}$

$4 x - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

$4 x - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

$4 x - 2 y = 14$

Step 2

Replace all occurrences of $x$ with $\frac{y}{2} - \frac{7}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $4 x - 2 y = 14$ with $\frac{y}{2} - \frac{7}{2}$ .

$4 (\frac{y}{2} - \frac{7}{2}) - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $4 (\frac{y}{2} - \frac{7}{2}) - 2 y$ .

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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.

$4 (\frac{y}{2}) + 4 (- \frac{7}{2}) - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Factor $2$ out of $4$ .

$2 (2) (\frac{y}{2}) + 4 (- \frac{7}{2}) - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 2.2.1.1.2.2

Cancel the common factor.

$2 \cdot (2 (\frac{y}{2})) + 4 (- \frac{7}{2}) - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 2.2.1.1.2.3

Rewrite the expression.

$2 y + 4 (- \frac{7}{2}) - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

$2 y + 4 (- \frac{7}{2}) - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 2.2.1.1.3

Cancel the common factor of $2$ .

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Step 2.2.1.1.3.1

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$2 y + 4 (\frac{- 7}{2}) - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 2.2.1.1.3.2

Factor $2$ out of $4$ .

$2 y + 2 (2) (\frac{- 7}{2}) - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 2.2.1.1.3.3

Cancel the common factor.

$2 y + 2 \cdot (2 (\frac{- 7}{2})) - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 2.2.1.1.3.4

Rewrite the expression.

$2 y + 2 \cdot - 7 - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

$2 y + 2 \cdot - 7 - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 2.2.1.1.4

Multiply $2$ by $- 7$ .

$2 y - 14 - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

$2 y - 14 - 2 y = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 2.2.1.2

Combine the opposite terms in $2 y - 14 - 2 y$ .

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Step 2.2.1.2.1

Subtract $2 y$ from $2 y$ .

$0 - 14 = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 2.2.1.2.2

Subtract $14$ from $0$ .

$- 14 = 14$

$x = \frac{y}{2} - \frac{7}{2}$

$- 14 = 14$

$x = \frac{y}{2} - \frac{7}{2}$

$- 14 = 14$

$x = \frac{y}{2} - \frac{7}{2}$

$- 14 = 14$

$x = \frac{y}{2} - \frac{7}{2}$

$- 14 = 14$

$x = \frac{y}{2} - \frac{7}{2}$

Step 3

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

No solution

Step 4