Finite Math Examples

$x + 2 y = 6$ , $y = 2 x + 3$

Step 1

Replace all occurrences of $y$ with $2 x + 3$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $x + 2 y = 6$ with $2 x + 3$ .

$x + 2 (2 x + 3) = 6$

$y = 2 x + 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $x + 2 (2 x + 3)$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$x + 2 (2 x) + 2 \cdot 3 = 6$

$y = 2 x + 3$

Step 1.2.1.1.2

Multiply $2$ by $2$ .

$x + 4 x + 2 \cdot 3 = 6$

$y = 2 x + 3$

Step 1.2.1.1.3

Multiply $2$ by $3$ .

$x + 4 x + 6 = 6$

$y = 2 x + 3$

$x + 4 x + 6 = 6$

$y = 2 x + 3$

Step 1.2.1.2

Add $x$ and $4 x$ .

$5 x + 6 = 6$

$y = 2 x + 3$

$5 x + 6 = 6$

$y = 2 x + 3$

$5 x + 6 = 6$

$y = 2 x + 3$

$5 x + 6 = 6$

$y = 2 x + 3$

Step 2

Solve for $x$ in $5 x + 6 = 6$ .

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Step 2.1

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

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Step 2.1.1

Subtract $6$ from both sides of the equation.

$5 x = 6 - 6$

$y = 2 x + 3$

Step 2.1.2

Subtract $6$ from $6$ .

$5 x = 0$

$y = 2 x + 3$

$5 x = 0$

$y = 2 x + 3$

Step 2.2

Divide each term in $5 x = 0$ by $5$ and simplify.

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Step 2.2.1

Divide each term in $5 x = 0$ by $5$ .

$\frac{5 x}{5} = \frac{0}{5}$

$y = 2 x + 3$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $5$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{0}{5}$

$y = 2 x + 3$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{5}$

$y = 2 x + 3$

$x = \frac{0}{5}$

$y = 2 x + 3$

$x = \frac{0}{5}$

$y = 2 x + 3$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $0$ by $5$ .

$x = 0$

$y = 2 x + 3$

$x = 0$

$y = 2 x + 3$

$x = 0$

$y = 2 x + 3$

$x = 0$

$y = 2 x + 3$

Step 3

Replace all occurrences of $x$ with $0$ in each equation.

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Step 3.1

Replace all occurrences of $x$ in $y = 2 x + 3$ with $0$ .

$y = 2 (0) + 3$

$x = 0$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $2 (0) + 3$ .

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Step 3.2.1.1

Multiply $2$ by $0$ .

$y = 0 + 3$

$x = 0$

Step 3.2.1.2

Add $0$ and $3$ .

$y = 3$

$x = 0$

$y = 3$

$x = 0$

$y = 3$

$x = 0$

$y = 3$

$x = 0$

Step 4

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

$(0, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, 3)$

Equation Form:

$x = 0, y = 3$

Step 6