Finite Math Examples

$2 x + y = 10$ , $x + y = 7$ , $x + 2 y = 12$ , $x y = 0$

Step 1

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

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Step 1.1

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

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

$2 x + y = 10$

$x + y = 7$

$x + 2 y = 12$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $y$ .

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Step 1.2.1.1

Cancel the common factor.

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

$2 x + y = 10$

$x + y = 7$

$x + 2 y = 12$

Step 1.2.1.2

Divide $x$ by $1$ .

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

$2 x + y = 10$

$x + y = 7$

$x + 2 y = 12$

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

$2 x + y = 10$

$x + y = 7$

$x + 2 y = 12$

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

$2 x + y = 10$

$x + y = 7$

$x + 2 y = 12$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $0$ by $y$ .

$x = 0$

$2 x + y = 10$

$x + y = 7$

$x + 2 y = 12$

$x = 0$

$2 x + y = 10$

$x + y = 7$

$x + 2 y = 12$

$x = 0$

$2 x + y = 10$

$x + y = 7$

$x + 2 y = 12$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $2 x + y = 10$ with $0$ .

$2 (0) + y = 10$

$x = 0$

$x + y = 7$

$x + 2 y = 12$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 (0) + y$ .

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Step 2.2.1.1

Multiply $2$ by $0$ .

$0 + y = 10$

$x = 0$

$x + y = 7$

$x + 2 y = 12$

Step 2.2.1.2

Add $0$ and $y$ .

$y = 10$

$x = 0$

$x + y = 7$

$x + 2 y = 12$

$y = 10$

$x = 0$

$x + y = 7$

$x + 2 y = 12$

$y = 10$

$x = 0$

$x + y = 7$

$x + 2 y = 12$

Step 2.3

Replace all occurrences of $x$ in $x + y = 7$ with $0$ .

$(0) + y = 7$

$y = 10$

$x = 0$

$x + 2 y = 12$

Step 2.4

Simplify the left side.

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Step 2.4.1

Add $0$ and $y$ .

$y = 7$

$y = 10$

$x = 0$

$x + 2 y = 12$

$y = 7$

$y = 10$

$x = 0$

$x + 2 y = 12$

Step 2.5

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

$(0) + 2 y = 12$

$y = 7$

$y = 10$

$x = 0$

Step 2.6

Simplify the left side.

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Step 2.6.1

Add $0$ and $2 y$ .

$2 y = 12$

$y = 7$

$y = 10$

$x = 0$

$2 y = 12$

$y = 7$

$y = 10$

$x = 0$

$2 y = 12$

$y = 7$

$y = 10$

$x = 0$

Step 3

Replace all occurrences of $y$ with $7$ in each equation.

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Step 3.1

Replace all occurrences of $y$ in $2 y = 12$ with $7$ .

$2 (7) = 12$

$y = 7$

$y = 10$

$x = 0$

Step 3.2

Simplify the left side.

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Step 3.2.1

Multiply $2$ by $7$ .

$14 = 12$

$y = 7$

$y = 10$

$x = 0$

$14 = 12$

$y = 7$

$y = 10$

$x = 0$

$14 = 12$

$y = 7$

$y = 10$

$x = 0$

Step 4

Since $14 = 12$ is not true, there is no solution.

No solution

Step 5