Finite Math Examples

$x + 3 y = 15$ , $2 x + y = 12$ , $x = 0$ , $y = 0$

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 $x + 3 y = 15$ with $0$ .

$(0) + 3 y = 15$

$x = 0$

$2 x + y = 12$

$y = 0$

Step 1.2

Simplify the left side.

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Step 1.2.1

Add $0$ and $3 y$ .

$3 y = 15$

$x = 0$

$2 x + y = 12$

$y = 0$

$3 y = 15$

$x = 0$

$2 x + y = 12$

$y = 0$

Step 1.3

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

$2 (0) + y = 12$

$3 y = 15$

$x = 0$

$y = 0$

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 $0$ .

$0 + y = 12$

$3 y = 15$

$x = 0$

$y = 0$

Step 1.4.1.2

Add $0$ and $y$ .

$y = 12$

$3 y = 15$

$x = 0$

$y = 0$

$y = 12$

$3 y = 15$

$x = 0$

$y = 0$

$y = 12$

$3 y = 15$

$x = 0$

$y = 0$

$y = 12$

$3 y = 15$

$x = 0$

$y = 0$

Step 2

Replace all occurrences of $y$ with $12$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $3 y = 15$ with $12$ .

$3 (12) = 15$

$y = 12$

$x = 0$

$y = 0$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $3$ by $12$ .

$36 = 15$

$y = 12$

$x = 0$

$y = 0$

$36 = 15$

$y = 12$

$x = 0$

$y = 0$

$36 = 15$

$y = 12$

$x = 0$

$y = 0$

Step 3

Since $36 = 15$ is not true, there is no solution.

No solution

Step 4