Finite Math Examples

$f (x) = 5 x + 2 y$ , $x + 2 y = 6$ , $2 x + y = 6$

Step 1

Solve for $f$ in $f (x) = 5 x + 2 y$ .

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Step 1.1

Subtract $f (x)$ from both sides of the equation.

$0 = 5 x + 2 y - f (x)$

$x + 2 y = 6$

$2 x + y = 6$

Step 1.2

Rewrite the equation as $5 x + 2 y - f (x) = 0$ .

$5 x + 2 y - f (x) = 0$

$x + 2 y = 6$

$2 x + y = 6$

$5 x + 2 y - f (x) = 0$

$x + 2 y = 6$

$2 x + y = 6$

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 $x + 2 y = 6$ with $0$ .

$(0) + 2 y = 6$

$5 x + 2 y - f (x) = 0$

$2 x + y = 6$

Step 2.2

Simplify the left side.

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Step 2.2.1

Add $0$ and $2 y$ .

$2 y = 6$

$5 x + 2 y - f (x) = 0$

$2 x + y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

$2 x + y = 6$

Step 2.3

Replace all occurrences of $x$ in $2 x + y = 6$ with $0$ .

$2 (0) + y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $2 (0) + y$ .

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Step 2.4.1.1

Multiply $2$ by $0$ .

$0 + y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

Step 2.4.1.2

Add $0$ and $y$ .

$y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

$y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

$y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

$y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

Step 3

Replace all occurrences of $y$ with $6$ in each equation.

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Step 3.1

Replace all occurrences of $y$ in $2 y = 6$ with $6$ .

$2 (6) = 6$

$y = 6$

$5 x + 2 y - f (x) = 0$

Step 3.2

Simplify the left side.

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Step 3.2.1

Multiply $2$ by $6$ .

$12 = 6$

$y = 6$

$5 x + 2 y - f (x) = 0$

$12 = 6$

$y = 6$

$5 x + 2 y - f (x) = 0$

Step 3.3

Replace all occurrences of $y$ in $5 x + 2 y - f (x) = 0$ with $6$ .

$5 x + 2 (6) - f (x) = 0$

$12 = 6$

$y = 6$

Step 3.4

Simplify the left side.

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Step 3.4.1

Multiply $2$ by $6$ .

$5 x + 12 - f (x) = 0$

$12 = 6$

$y = 6$

$5 x + 12 - f (x) = 0$

$12 = 6$

$y = 6$

$5 x + 12 - f (x) = 0$

$12 = 6$

$y = 6$

Step 4

Since $12 = 6$ is not true, there is no solution.

No solution

Step 5

Solve for $f$ in $f (x) = 5 x + 2 y$ .

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Step 5.1

Subtract $f (x)$ from both sides of the equation.

$0 = 5 x + 2 y - f (x)$

$x + 2 y = 6$

$2 x + y = 6$

Step 5.2

Rewrite the equation as $5 x + 2 y - f (x) = 0$ .

$5 x + 2 y - f (x) = 0$

$x + 2 y = 6$

$2 x + y = 6$

$5 x + 2 y - f (x) = 0$

$x + 2 y = 6$

$2 x + y = 6$

Step 6

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

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Step 6.1

Replace all occurrences of $x$ in $x + 2 y = 6$ with $0$ .

$(0) + 2 y = 6$

$5 x + 2 y - f (x) = 0$

$2 x + y = 6$

Step 6.2

Simplify the left side.

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Step 6.2.1

Add $0$ and $2 y$ .

$2 y = 6$

$5 x + 2 y - f (x) = 0$

$2 x + y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

$2 x + y = 6$

Step 6.3

Replace all occurrences of $x$ in $2 x + y = 6$ with $0$ .

$2 (0) + y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

Step 6.4

Simplify the left side.

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Step 6.4.1

Simplify $2 (0) + y$ .

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Step 6.4.1.1

Multiply $2$ by $0$ .

$0 + y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

Step 6.4.1.2

Add $0$ and $y$ .

$y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

$y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

$y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

$y = 6$

$2 y = 6$

$5 x + 2 y - f (x) = 0$

Step 7

Replace all occurrences of $y$ with $6$ in each equation.

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Step 7.1

Replace all occurrences of $y$ in $2 y = 6$ with $6$ .

$2 (6) = 6$

$y = 6$

$5 x + 2 y - f (x) = 0$

Step 7.2

Simplify the left side.

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Step 7.2.1

Multiply $2$ by $6$ .

$12 = 6$

$y = 6$

$5 x + 2 y - f (x) = 0$

$12 = 6$

$y = 6$

$5 x + 2 y - f (x) = 0$

Step 7.3

Replace all occurrences of $y$ in $5 x + 2 y - f (x) = 0$ with $6$ .

$5 x + 2 (6) - f (x) = 0$

$12 = 6$

$y = 6$

Step 7.4

Simplify the left side.

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Step 7.4.1

Multiply $2$ by $6$ .

$5 x + 12 - f (x) = 0$

$12 = 6$

$y = 6$

$5 x + 12 - f (x) = 0$

$12 = 6$

$y = 6$

$5 x + 12 - f (x) = 0$

$12 = 6$

$y = 6$

Step 8

Since $12 = 6$ is not true, there is no solution.

No solution