Finite Math Examples

$x + 16 y = 9$ , $\frac{1}{4} x + 4 y = 8$

Step 1

Subtract $16 y$ from both sides of the equation.

$x = 9 - 16 y$

$\frac{1}{4} x + 4 y = 8$

Step 2

Replace all occurrences of $x$ with $9 - 16 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $\frac{1}{4} x + 4 y = 8$ with $9 - 16 y$ .

$\frac{1}{4} \cdot (9 - 16 y) + 4 y = 8$

$x = 9 - 16 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $\frac{1}{4} \cdot (9 - 16 y) + 4 y$ .

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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.

$\frac{1}{4} \cdot 9 + \frac{1}{4} \cdot (- 16 y) + 4 y = 8$

$x = 9 - 16 y$

Step 2.2.1.1.2

Combine $\frac{1}{4}$ and $9$ .

$\frac{9}{4} + \frac{1}{4} \cdot (- 16 y) + 4 y = 8$

$x = 9 - 16 y$

Step 2.2.1.1.3

Cancel the common factor of $4$ .

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Step 2.2.1.1.3.1

Factor $4$ out of $- 16 y$ .

$\frac{9}{4} + \frac{1}{4} \cdot (4 (- 4 y)) + 4 y = 8$

$x = 9 - 16 y$

Step 2.2.1.1.3.2

Cancel the common factor.

$\frac{9}{4} + \frac{1}{4} \cdot (4 (- 4 y)) + 4 y = 8$

$x = 9 - 16 y$

Step 2.2.1.1.3.3

Rewrite the expression.

$\frac{9}{4} - 4 y + 4 y = 8$

$x = 9 - 16 y$

$\frac{9}{4} - 4 y + 4 y = 8$

$x = 9 - 16 y$

$\frac{9}{4} - 4 y + 4 y = 8$

$x = 9 - 16 y$

Step 2.2.1.2

Combine the opposite terms in $\frac{9}{4} - 4 y + 4 y$ .

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Step 2.2.1.2.1

Add $- 4 y$ and $4 y$ .

$\frac{9}{4} + 0 = 8$

$x = 9 - 16 y$

Step 2.2.1.2.2

Add $\frac{9}{4}$ and $0$ .

$\frac{9}{4} = 8$

$x = 9 - 16 y$

$\frac{9}{4} = 8$

$x = 9 - 16 y$

$\frac{9}{4} = 8$

$x = 9 - 16 y$

$\frac{9}{4} = 8$

$x = 9 - 16 y$

$\frac{9}{4} = 8$

$x = 9 - 16 y$

Step 3

Since $\frac{9}{4} = 8$ is not true, there is no solution.

No solution

Step 4