Finite Math Examples

$2 x + y = 12$ , $x + y = 8$ , $x + 2 y = 14$

Step 1

Subtract $2 x$ from both sides of the equation.

$y = 12 - 2 x$

$x + y = 8$

$x + 2 y = 14$

Step 2

Replace all occurrences of $y$ with $12 - 2 x$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $y$ in $x + y = 8$ with $12 - 2 x$ .

$x + 12 - 2 x = 8$

$y = 12 - 2 x$

$x + 2 y = 14$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $x + 12 - 2 x$ .

Tap for more steps...

Step 2.2.1.1

Remove parentheses.

$x + 12 - 2 x = 8$

$y = 12 - 2 x$

$x + 2 y = 14$

Step 2.2.1.2

Subtract $2 x$ from $x$ .

$- x + 12 = 8$

$y = 12 - 2 x$

$x + 2 y = 14$

$- x + 12 = 8$

$y = 12 - 2 x$

$x + 2 y = 14$

$- x + 12 = 8$

$y = 12 - 2 x$

$x + 2 y = 14$

Step 2.3

Replace all occurrences of $y$ in $x + 2 y = 14$ with $12 - 2 x$ .

$x + 2 (12 - 2 x) = 14$

$- x + 12 = 8$

$y = 12 - 2 x$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $x + 2 (12 - 2 x)$ .

Tap for more steps...

Step 2.4.1.1

Simplify each term.

Tap for more steps...

Step 2.4.1.1.1

Apply the distributive property.

$x + 2 \cdot 12 + 2 (- 2 x) = 14$

$- x + 12 = 8$

$y = 12 - 2 x$

Step 2.4.1.1.2

Multiply $2$ by $12$ .

$x + 24 + 2 (- 2 x) = 14$

$- x + 12 = 8$

$y = 12 - 2 x$

Step 2.4.1.1.3

Multiply $- 2$ by $2$ .

$x + 24 - 4 x = 14$

$- x + 12 = 8$

$y = 12 - 2 x$

$x + 24 - 4 x = 14$

$- x + 12 = 8$

$y = 12 - 2 x$

Step 2.4.1.2

Subtract $4 x$ from $x$ .

$- 3 x + 24 = 14$

$- x + 12 = 8$

$y = 12 - 2 x$

$- 3 x + 24 = 14$

$- x + 12 = 8$

$y = 12 - 2 x$

$- 3 x + 24 = 14$

$- x + 12 = 8$

$y = 12 - 2 x$

$- 3 x + 24 = 14$

$- x + 12 = 8$

$y = 12 - 2 x$

Step 3

Solve for $x$ in $- 3 x + 24 = 14$ .

Tap for more steps...

Step 3.1

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 3.1.1

Subtract $24$ from both sides of the equation.

$- 3 x = 14 - 24$

$- x + 12 = 8$

$y = 12 - 2 x$

Step 3.1.2

Subtract $24$ from $14$ .

$- 3 x = - 10$

$- x + 12 = 8$

$y = 12 - 2 x$

$- 3 x = - 10$

$- x + 12 = 8$

$y = 12 - 2 x$

Step 3.2

Divide each term in $- 3 x = - 10$ by $- 3$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 3 x = - 10$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 10}{- 3}$

$- x + 12 = 8$

$y = 12 - 2 x$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 10}{- 3}$

$- x + 12 = 8$

$y = 12 - 2 x$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 10}{- 3}$

$- x + 12 = 8$

$y = 12 - 2 x$

$x = \frac{- 10}{- 3}$

$- x + 12 = 8$

$y = 12 - 2 x$

$x = \frac{- 10}{- 3}$

$- x + 12 = 8$

$y = 12 - 2 x$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Dividing two negative values results in a positive value.

$x = \frac{10}{3}$

$- x + 12 = 8$

$y = 12 - 2 x$

$x = \frac{10}{3}$

$- x + 12 = 8$

$y = 12 - 2 x$

$x = \frac{10}{3}$

$- x + 12 = 8$

$y = 12 - 2 x$

$x = \frac{10}{3}$

$- x + 12 = 8$

$y = 12 - 2 x$

Step 4

Replace all occurrences of $x$ with $\frac{10}{3}$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $x$ in $- x + 12 = 8$ with $\frac{10}{3}$ .

$- (\frac{10}{3}) + 12 = 8$

$x = \frac{10}{3}$

$y = 12 - 2 x$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Simplify $- (\frac{10}{3}) + 12$ .

Tap for more steps...

Step 4.2.1.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{10}{3} + 12 \cdot \frac{3}{3} = 8$

$x = \frac{10}{3}$

$y = 12 - 2 x$

Step 4.2.1.2

Combine $12$ and $\frac{3}{3}$ .

$- \frac{10}{3} + \frac{12 \cdot 3}{3} = 8$

$x = \frac{10}{3}$

$y = 12 - 2 x$

Step 4.2.1.3

Combine the numerators over the common denominator.

$\frac{- 10 + 12 \cdot 3}{3} = 8$

$x = \frac{10}{3}$

$y = 12 - 2 x$

Step 4.2.1.4

Simplify the numerator.

Tap for more steps...

Step 4.2.1.4.1

Multiply $12$ by $3$ .

$\frac{- 10 + 36}{3} = 8$

$x = \frac{10}{3}$

$y = 12 - 2 x$

Step 4.2.1.4.2

Add $- 10$ and $36$ .

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

$y = 12 - 2 x$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

$y = 12 - 2 x$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

$y = 12 - 2 x$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

$y = 12 - 2 x$

Step 4.3

Replace all occurrences of $x$ in $y = 12 - 2 x$ with $\frac{10}{3}$ .

$y = 12 - 2 (\frac{10}{3})$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

Step 4.4

Simplify the right side.

Tap for more steps...

Step 4.4.1

Simplify $12 - 2 (\frac{10}{3})$ .

Tap for more steps...

Step 4.4.1.1

Simplify each term.

Tap for more steps...

Step 4.4.1.1.1

Multiply $- 2 (\frac{10}{3})$ .

Tap for more steps...

Step 4.4.1.1.1.1

Combine $- 2$ and $\frac{10}{3}$ .

$y = 12 + \frac{- 2 \cdot 10}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

Step 4.4.1.1.1.2

Multiply $- 2$ by $10$ .

$y = 12 + \frac{- 20}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

$y = 12 + \frac{- 20}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

Step 4.4.1.1.2

Move the negative in front of the fraction.

$y = 12 - \frac{20}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

$y = 12 - \frac{20}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

Step 4.4.1.2

To write $12$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = 12 \cdot \frac{3}{3} - \frac{20}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

Step 4.4.1.3

Combine $12$ and $\frac{3}{3}$ .

$y = \frac{12 \cdot 3}{3} - \frac{20}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$y = \frac{12 \cdot 3 - 20}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

Step 4.4.1.5

Simplify the numerator.

Tap for more steps...

Step 4.4.1.5.1

Multiply $12$ by $3$ .

$y = \frac{36 - 20}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

Step 4.4.1.5.2

Subtract $20$ from $36$ .

$y = \frac{16}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

$y = \frac{16}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

$y = \frac{16}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

$y = \frac{16}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

$y = \frac{16}{3}$

$\frac{26}{3} = 8$

$x = \frac{10}{3}$

Step 5

Since $\frac{26}{3} = 8$ is not true, there is no solution.

No solution

Step 6