Finite Math Examples

$x + y = 8$ , $2 x + y = 12$ , $x + y = 11$ , $x = 0$ , $y = 0$

Step 1

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

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Step 1.1

Replace all occurrences of $x$ in $x + y = 8$ with $0$ .

$(0) + y = 8$

$x = 0$

$2 x + y = 12$

$x + y = 11$

$y = 0$

Step 1.2

Simplify the left side.

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Step 1.2.1

Add $0$ and $y$ .

$y = 8$

$x = 0$

$2 x + y = 12$

$x + y = 11$

$y = 0$

$y = 8$

$x = 0$

$2 x + y = 12$

$x + y = 11$

$y = 0$

Step 1.3

Replace all occurrences of $x$ in $2 x + y = 12$ with $0$ .

$2 (0) + y = 12$

$y = 8$

$x = 0$

$x + y = 11$

$y = 0$

Step 1.4

Simplify the left side.

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Step 1.4.1

Simplify $2 (0) + y$ .

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Step 1.4.1.1

Multiply $2$ by $0$ .

$0 + y = 12$

$y = 8$

$x = 0$

$x + y = 11$

$y = 0$

Step 1.4.1.2

Add $0$ and $y$ .

$y = 12$

$y = 8$

$x = 0$

$x + y = 11$

$y = 0$

$y = 12$

$y = 8$

$x = 0$

$x + y = 11$

$y = 0$

$y = 12$

$y = 8$

$x = 0$

$x + y = 11$

$y = 0$

Step 1.5

Replace all occurrences of $x$ in $x + y = 11$ with $0$ .

$(0) + y = 11$

$y = 12$

$y = 8$

$x = 0$

$y = 0$

Step 1.6

Simplify the left side.

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Step 1.6.1

Add $0$ and $y$ .

$y = 11$

$y = 12$

$y = 8$

$x = 0$

$y = 0$

$y = 11$

$y = 12$

$y = 8$

$x = 0$

$y = 0$

$y = 11$

$y = 12$

$y = 8$

$x = 0$

$y = 0$

Step 2

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

$(0, 8)$

Step 3

The result can be shown in multiple forms.

Point Form:

$(0, 8)$

Equation Form:

$x = 0, y = 8$

Step 4