Finite Math Examples

$2 x - 8 y = 3$ , $- 16 x + 64 y = - 23$

Step 1

Solve for $x$ in $2 x - 8 y = 3$ .

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Step 1.1

Add $8 y$ to both sides of the equation.

$2 x = 3 + 8 y$

$- 16 x + 64 y = - 23$

Step 1.2

Divide each term in $2 x = 3 + 8 y$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x = 3 + 8 y$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2} + \frac{8 y}{2}$

$- 16 x + 64 y = - 23$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2} + \frac{8 y}{2}$

$- 16 x + 64 y = - 23$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{2} + \frac{8 y}{2}$

$- 16 x + 64 y = - 23$

$x = \frac{3}{2} + \frac{8 y}{2}$

$- 16 x + 64 y = - 23$

$x = \frac{3}{2} + \frac{8 y}{2}$

$- 16 x + 64 y = - 23$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Cancel the common factor of $8$ and $2$ .

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Step 1.2.3.1.1

Factor $2$ out of $8 y$ .

$x = \frac{3}{2} + \frac{2 (4 y)}{2}$

$- 16 x + 64 y = - 23$

Step 1.2.3.1.2

Cancel the common factors.

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Step 1.2.3.1.2.1

Factor $2$ out of $2$ .

$x = \frac{3}{2} + \frac{2 (4 y)}{2 (1)}$

$- 16 x + 64 y = - 23$

Step 1.2.3.1.2.2

Cancel the common factor.

$x = \frac{3}{2} + \frac{2 (4 y)}{2 \cdot 1}$

$- 16 x + 64 y = - 23$

Step 1.2.3.1.2.3

Rewrite the expression.

$x = \frac{3}{2} + \frac{4 y}{1}$

$- 16 x + 64 y = - 23$

Step 1.2.3.1.2.4

Divide $4 y$ by $1$ .

$x = \frac{3}{2} + 4 y$

$- 16 x + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

$- 16 x + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

$- 16 x + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

$- 16 x + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

$- 16 x + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

$- 16 x + 64 y = - 23$

Step 2

Replace all occurrences of $x$ with $\frac{3}{2} + 4 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 16 x + 64 y = - 23$ with $\frac{3}{2} + 4 y$ .

$- 16 (\frac{3}{2} + 4 y) + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 16 (\frac{3}{2} + 4 y) + 64 y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$- 16 (\frac{3}{2}) - 16 (4 y) + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Factor $2$ out of $- 16$ .

$2 (- 8) (\frac{3}{2}) - 16 (4 y) + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

Step 2.2.1.1.2.2

Cancel the common factor.

$2 \cdot (- 8 (\frac{3}{2})) - 16 (4 y) + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

Step 2.2.1.1.2.3

Rewrite the expression.

$- 8 \cdot 3 - 16 (4 y) + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

$- 8 \cdot 3 - 16 (4 y) + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

Step 2.2.1.1.3

Multiply $- 8$ by $3$ .

$- 24 - 16 (4 y) + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

Step 2.2.1.1.4

Multiply $4$ by $- 16$ .

$- 24 - 64 y + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

$- 24 - 64 y + 64 y = - 23$

$x = \frac{3}{2} + 4 y$

Step 2.2.1.2

Combine the opposite terms in $- 24 - 64 y + 64 y$ .

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Step 2.2.1.2.1

Add $- 64 y$ and $64 y$ .

$- 24 + 0 = - 23$

$x = \frac{3}{2} + 4 y$

Step 2.2.1.2.2

Add $- 24$ and $0$ .

$- 24 = - 23$

$x = \frac{3}{2} + 4 y$

$- 24 = - 23$

$x = \frac{3}{2} + 4 y$

$- 24 = - 23$

$x = \frac{3}{2} + 4 y$

$- 24 = - 23$

$x = \frac{3}{2} + 4 y$

$- 24 = - 23$

$x = \frac{3}{2} + 4 y$

Step 3

Since $- 24 = - 23$ is not true, there is no solution.

No solution

Step 4