Finite Math Examples

$2 x + y = 15$ , $3 x + y = 20$

Step 1

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

$y = 15 - 2 x$

$3 x + y = 20$

Step 2

Replace all occurrences of $y$ with $15 - 2 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $3 x + y = 20$ with $15 - 2 x$ .

$3 x + 15 - 2 x = 20$

$y = 15 - 2 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 x + 15 - 2 x$ .

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Step 2.2.1.1

Remove parentheses.

$3 x + 15 - 2 x = 20$

$y = 15 - 2 x$

Step 2.2.1.2

Subtract $2 x$ from $3 x$ .

$x + 15 = 20$

$y = 15 - 2 x$

$x + 15 = 20$

$y = 15 - 2 x$

$x + 15 = 20$

$y = 15 - 2 x$

$x + 15 = 20$

$y = 15 - 2 x$

Step 3

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

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Step 3.1

Subtract $15$ from both sides of the equation.

$x = 20 - 15$

$y = 15 - 2 x$

Step 3.2

Subtract $15$ from $20$ .

$x = 5$

$y = 15 - 2 x$

$x = 5$

$y = 15 - 2 x$

Step 4

Replace all occurrences of $x$ with $5$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = 15 - 2 x$ with $5$ .

$y = 15 - 2 \cdot 5$

$x = 5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $15 - 2 \cdot 5$ .

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Step 4.2.1.1

Multiply $- 2$ by $5$ .

$y = 15 - 10$

$x = 5$

Step 4.2.1.2

Subtract $10$ from $15$ .

$y = 5$

$x = 5$

$y = 5$

$x = 5$

$y = 5$

$x = 5$

$y = 5$

$x = 5$

Step 5

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

$(5, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, 5)$

Equation Form:

$x = 5, y = 5$

Step 7