Finite Math Examples

$68 = 2 x + 3 y$ , $25 = x + y$

Step 1

Solve for $x$ in $25 = x + y$ .

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Step 1.1

Rewrite the equation as $x + y = 25$ .

$x + y = 25$

$68 = 2 x + 3 y$

Step 1.2

Subtract $y$ from both sides of the equation.

$x = 25 - y$

$68 = 2 x + 3 y$

$x = 25 - y$

$68 = 2 x + 3 y$

Step 2

Replace all occurrences of $x$ with $25 - y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $68 = 2 x + 3 y$ with $25 - y$ .

$68 = 2 (25 - y) + 3 y$

$x = 25 - y$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $2 (25 - y) + 3 y$ .

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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.

$68 = 2 \cdot 25 + 2 (- y) + 3 y$

$x = 25 - y$

Step 2.2.1.1.2

Multiply $2$ by $25$ .

$68 = 50 + 2 (- y) + 3 y$

$x = 25 - y$

Step 2.2.1.1.3

Multiply $- 1$ by $2$ .

$68 = 50 - 2 y + 3 y$

$x = 25 - y$

$68 = 50 - 2 y + 3 y$

$x = 25 - y$

Step 2.2.1.2

Add $- 2 y$ and $3 y$ .

$68 = 50 + y$

$x = 25 - y$

$68 = 50 + y$

$x = 25 - y$

$68 = 50 + y$

$x = 25 - y$

$68 = 50 + y$

$x = 25 - y$

Step 3

Solve for $y$ in $68 = 50 + y$ .

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Step 3.1

Rewrite the equation as $50 + y = 68$ .

$50 + y = 68$

$x = 25 - y$

Step 3.2

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

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Step 3.2.1

Subtract $50$ from both sides of the equation.

$y = 68 - 50$

$x = 25 - y$

Step 3.2.2

Subtract $50$ from $68$ .

$y = 18$

$x = 25 - y$

$y = 18$

$x = 25 - y$

$y = 18$

$x = 25 - y$

Step 4

Replace all occurrences of $y$ with $18$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 25 - y$ with $18$ .

$x = 25 - (18)$

$y = 18$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $25 - (18)$ .

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Step 4.2.1.1

Multiply $- 1$ by $18$ .

$x = 25 - 18$

$y = 18$

Step 4.2.1.2

Subtract $18$ from $25$ .

$x = 7$

$y = 18$

$x = 7$

$y = 18$

$x = 7$

$y = 18$

$x = 7$

$y = 18$

Step 5

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

$(7, 18)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(7, 18)$

Equation Form:

$x = 7, y = 18$

Step 7