Finite Math Examples

$x + y = 17$ , $x + 2 y = 20$

Step 1

Subtract $y$ from both sides of the equation.

$x = 17 - y$

$x + 2 y = 20$

Step 2

Replace all occurrences of $x$ with $17 - y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $x + 2 y = 20$ with $17 - y$ .

$(17 - y) + 2 y = 20$

$x = 17 - y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Add $- y$ and $2 y$ .

$17 + y = 20$

$x = 17 - y$

$17 + y = 20$

$x = 17 - y$

$17 + y = 20$

$x = 17 - y$

Step 3

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

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Step 3.1

Subtract $17$ from both sides of the equation.

$y = 20 - 17$

$x = 17 - y$

Step 3.2

Subtract $17$ from $20$ .

$y = 3$

$x = 17 - y$

$y = 3$

$x = 17 - y$

Step 4

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

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Step 4.1

Replace all occurrences of $y$ in $x = 17 - y$ with $3$ .

$x = 17 - (3)$

$y = 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $17 - (3)$ .

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Step 4.2.1.1

Multiply $- 1$ by $3$ .

$x = 17 - 3$

$y = 3$

Step 4.2.1.2

Subtract $3$ from $17$ .

$x = 14$

$y = 3$

$x = 14$

$y = 3$

$x = 14$

$y = 3$

$x = 14$

$y = 3$

Step 5

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

$(14, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(14, 3)$

Equation Form:

$x = 14, y = 3$

Step 7