Finite Math Examples

$x + 2 y = 7$ , $4 x - 6 y = 7$

Step 1

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

$x = 7 - 2 y$

$4 x - 6 y = 7$

Step 2

Replace all occurrences of $x$ with $7 - 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $4 x - 6 y = 7$ with $7 - 2 y$ .

$4 (7 - 2 y) - 6 y = 7$

$x = 7 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $4 (7 - 2 y) - 6 y$ .

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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.

$4 \cdot 7 + 4 (- 2 y) - 6 y = 7$

$x = 7 - 2 y$

Step 2.2.1.1.2

Multiply $4$ by $7$ .

$28 + 4 (- 2 y) - 6 y = 7$

$x = 7 - 2 y$

Step 2.2.1.1.3

Multiply $- 2$ by $4$ .

$28 - 8 y - 6 y = 7$

$x = 7 - 2 y$

$28 - 8 y - 6 y = 7$

$x = 7 - 2 y$

Step 2.2.1.2

Subtract $6 y$ from $- 8 y$ .

$28 - 14 y = 7$

$x = 7 - 2 y$

$28 - 14 y = 7$

$x = 7 - 2 y$

$28 - 14 y = 7$

$x = 7 - 2 y$

$28 - 14 y = 7$

$x = 7 - 2 y$

Step 3

Solve for $y$ in $28 - 14 y = 7$ .

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Step 3.1

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

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Step 3.1.1

Subtract $28$ from both sides of the equation.

$- 14 y = 7 - 28$

$x = 7 - 2 y$

Step 3.1.2

Subtract $28$ from $7$ .

$- 14 y = - 21$

$x = 7 - 2 y$

$- 14 y = - 21$

$x = 7 - 2 y$

Step 3.2

Divide each term in $- 14 y = - 21$ by $- 14$ and simplify.

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Step 3.2.1

Divide each term in $- 14 y = - 21$ by $- 14$ .

$\frac{- 14 y}{- 14} = \frac{- 21}{- 14}$

$x = 7 - 2 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 14$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 14 y}{- 14} = \frac{- 21}{- 14}$

$x = 7 - 2 y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 21}{- 14}$

$x = 7 - 2 y$

$y = \frac{- 21}{- 14}$

$x = 7 - 2 y$

$y = \frac{- 21}{- 14}$

$x = 7 - 2 y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of $- 21$ and $- 14$ .

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Step 3.2.3.1.1

Factor $- 7$ out of $- 21$ .

$y = \frac{- 7 \cdot 3}{- 14}$

$x = 7 - 2 y$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor $- 7$ out of $- 14$ .

$y = \frac{- 7 \cdot 3}{- 7 \cdot 2}$

$x = 7 - 2 y$

Step 3.2.3.1.2.2

Cancel the common factor.

$y = \frac{- 7 \cdot 3}{- 7 \cdot 2}$

$x = 7 - 2 y$

Step 3.2.3.1.2.3

Rewrite the expression.

$y = \frac{3}{2}$

$x = 7 - 2 y$

$y = \frac{3}{2}$

$x = 7 - 2 y$

$y = \frac{3}{2}$

$x = 7 - 2 y$

$y = \frac{3}{2}$

$x = 7 - 2 y$

$y = \frac{3}{2}$

$x = 7 - 2 y$

$y = \frac{3}{2}$

$x = 7 - 2 y$

Step 4

Replace all occurrences of $y$ with $\frac{3}{2}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 7 - 2 y$ with $\frac{3}{2}$ .

$x = 7 - 2 (\frac{3}{2})$

$y = \frac{3}{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $7 - 2 (\frac{3}{2})$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1.1

Factor $2$ out of $- 2$ .

$x = 7 + 2 (- 1) (\frac{3}{2})$

$y = \frac{3}{2}$

Step 4.2.1.1.1.2

Cancel the common factor.

$x = 7 + 2 \cdot (- 1 (\frac{3}{2}))$

$y = \frac{3}{2}$

Step 4.2.1.1.1.3

Rewrite the expression.

$x = 7 - 1 \cdot 3$

$y = \frac{3}{2}$

$x = 7 - 1 \cdot 3$

$y = \frac{3}{2}$

Step 4.2.1.1.2

Multiply $- 1$ by $3$ .

$x = 7 - 3$

$y = \frac{3}{2}$

$x = 7 - 3$

$y = \frac{3}{2}$

Step 4.2.1.2

Subtract $3$ from $7$ .

$x = 4$

$y = \frac{3}{2}$

$x = 4$

$y = \frac{3}{2}$

$x = 4$

$y = \frac{3}{2}$

$x = 4$

$y = \frac{3}{2}$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(4, \frac{3}{2})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, \frac{3}{2})$

Equation Form:

$x = 4, y = \frac{3}{2}$

Step 7