Finite Math Examples

$7 x + 3 y = 25$ , $- 9 x + 2 y = 3$ , $x + 2 = 2$ , $- 3 x + 5 y = 66$

Step 1

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

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Step 1.1

Subtract $2$ from both sides of the equation.

$x = 2 - 2$

$7 x + 3 y = 25$

$- 9 x + 2 y = 3$

$- 3 x + 5 y = 66$

Step 1.2

Subtract $2$ from $2$ .

$x = 0$

$7 x + 3 y = 25$

$- 9 x + 2 y = 3$

$- 3 x + 5 y = 66$

$x = 0$

$7 x + 3 y = 25$

$- 9 x + 2 y = 3$

$- 3 x + 5 y = 66$

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 $7 x + 3 y = 25$ with $0$ .

$7 (0) + 3 y = 25$

$x = 0$

$- 9 x + 2 y = 3$

$- 3 x + 5 y = 66$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $7 (0) + 3 y$ .

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Step 2.2.1.1

Multiply $7$ by $0$ .

$0 + 3 y = 25$

$x = 0$

$- 9 x + 2 y = 3$

$- 3 x + 5 y = 66$

Step 2.2.1.2

Add $0$ and $3 y$ .

$3 y = 25$

$x = 0$

$- 9 x + 2 y = 3$

$- 3 x + 5 y = 66$

$3 y = 25$

$x = 0$

$- 9 x + 2 y = 3$

$- 3 x + 5 y = 66$

$3 y = 25$

$x = 0$

$- 9 x + 2 y = 3$

$- 3 x + 5 y = 66$

Step 2.3

Replace all occurrences of $x$ in $- 9 x + 2 y = 3$ with $0$ .

$- 9 \cdot 0 + 2 y = 3$

$3 y = 25$

$x = 0$

$- 3 x + 5 y = 66$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $- 9 \cdot 0 + 2 y$ .

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Step 2.4.1.1

Multiply $- 9$ by $0$ .

$0 + 2 y = 3$

$3 y = 25$

$x = 0$

$- 3 x + 5 y = 66$

Step 2.4.1.2

Add $0$ and $2 y$ .

$2 y = 3$

$3 y = 25$

$x = 0$

$- 3 x + 5 y = 66$

$2 y = 3$

$3 y = 25$

$x = 0$

$- 3 x + 5 y = 66$

$2 y = 3$

$3 y = 25$

$x = 0$

$- 3 x + 5 y = 66$

Step 2.5

Replace all occurrences of $x$ in $- 3 x + 5 y = 66$ with $0$ .

$- 3 \cdot 0 + 5 y = 66$

$2 y = 3$

$3 y = 25$

$x = 0$

Step 2.6

Simplify the left side.

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Step 2.6.1

Simplify $- 3 \cdot 0 + 5 y$ .

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Step 2.6.1.1

Multiply $- 3$ by $0$ .

$0 + 5 y = 66$

$2 y = 3$

$3 y = 25$

$x = 0$

Step 2.6.1.2

Add $0$ and $5 y$ .

$5 y = 66$

$2 y = 3$

$3 y = 25$

$x = 0$

$5 y = 66$

$2 y = 3$

$3 y = 25$

$x = 0$

$5 y = 66$

$2 y = 3$

$3 y = 25$

$x = 0$

$5 y = 66$

$2 y = 3$

$3 y = 25$

$x = 0$

Step 3

Divide each term in $5 y = 66$ by $5$ and simplify.

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Step 3.1

Divide each term in $5 y = 66$ by $5$ .

$\frac{5 y}{5} = \frac{66}{5}$

$2 y = 3$

$3 y = 25$

$x = 0$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{66}{5}$

$2 y = 3$

$3 y = 25$

$x = 0$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{66}{5}$

$2 y = 3$

$3 y = 25$

$x = 0$

$y = \frac{66}{5}$

$2 y = 3$

$3 y = 25$

$x = 0$

$y = \frac{66}{5}$

$2 y = 3$

$3 y = 25$

$x = 0$

$y = \frac{66}{5}$

$2 y = 3$

$3 y = 25$

$x = 0$

Step 4

Replace all occurrences of $y$ with $\frac{66}{5}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $2 y = 3$ with $\frac{66}{5}$ .

$2 (\frac{66}{5}) = 3$

$y = \frac{66}{5}$

$3 y = 25$

$x = 0$

Step 4.2

Simplify the left side.

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Step 4.2.1

Multiply $2 (\frac{66}{5})$ .

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Step 4.2.1.1

Combine $2$ and $\frac{66}{5}$ .

$\frac{2 \cdot 66}{5} = 3$

$y = \frac{66}{5}$

$3 y = 25$

$x = 0$

Step 4.2.1.2

Multiply $2$ by $66$ .

$\frac{132}{5} = 3$

$y = \frac{66}{5}$

$3 y = 25$

$x = 0$

$\frac{132}{5} = 3$

$y = \frac{66}{5}$

$3 y = 25$

$x = 0$

$\frac{132}{5} = 3$

$y = \frac{66}{5}$

$3 y = 25$

$x = 0$

Step 4.3

Replace all occurrences of $y$ in $3 y = 25$ with $\frac{66}{5}$ .

$3 (\frac{66}{5}) = 25$

$\frac{132}{5} = 3$

$y = \frac{66}{5}$

$x = 0$

Step 4.4

Simplify the left side.

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Step 4.4.1

Multiply $3 (\frac{66}{5})$ .

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Step 4.4.1.1

Combine $3$ and $\frac{66}{5}$ .

$\frac{3 \cdot 66}{5} = 25$

$\frac{132}{5} = 3$

$y = \frac{66}{5}$

$x = 0$

Step 4.4.1.2

Multiply $3$ by $66$ .

$\frac{198}{5} = 25$

$\frac{132}{5} = 3$

$y = \frac{66}{5}$

$x = 0$

$\frac{198}{5} = 25$

$\frac{132}{5} = 3$

$y = \frac{66}{5}$

$x = 0$

$\frac{198}{5} = 25$

$\frac{132}{5} = 3$

$y = \frac{66}{5}$

$x = 0$

$\frac{198}{5} = 25$

$\frac{132}{5} = 3$

$y = \frac{66}{5}$

$x = 0$

Step 5

Since $\frac{198}{5} = 25$ is not true, there is no solution.

No solution

Step 6