Precalculus Examples

$(\frac{5}{4}, 1)$ , $4 x - 3 y = 8$ , $- 11 x + 4 y = 11$

Step 1

Simplify $4 (\frac{5}{4}) - 3 \cdot 1$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $4$ .

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Step 1.1.1.1

Cancel the common factor.

$4 (\frac{5}{4}) - 3 \cdot 1 = 8$

$- 11 (\frac{5}{4}) + 4 (1) = 11$

Step 1.1.1.2

Rewrite the expression.

$5 - 3 \cdot 1 = 8$

$- 11 (\frac{5}{4}) + 4 (1) = 11$

$5 - 3 \cdot 1 = 8$

$- 11 (\frac{5}{4}) + 4 (1) = 11$

Step 1.1.2

Multiply $- 3$ by $1$ .

$5 - 3 = 8$

$- 11 (\frac{5}{4}) + 4 (1) = 11$

$5 - 3 = 8$

$- 11 (\frac{5}{4}) + 4 (1) = 11$

Step 1.2

Subtract $3$ from $5$ .

$2 = 8$

$- 11 (\frac{5}{4}) + 4 (1) = 11$

$2 = 8$

$- 11 (\frac{5}{4}) + 4 (1) = 11$

Step 2

Since $2 \neq 8$ , there are no solutions.

No solution

Step 3

Simplify $- 11 (\frac{5}{4}) + 4 (1)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $- 11 (\frac{5}{4})$ .

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Step 3.1.1.1

Combine $- 11$ and $\frac{5}{4}$ .

$\frac{- 11 \cdot 5}{4} + 4 (1) = 11$

No solution

Step 3.1.1.2

Multiply $- 11$ by $5$ .

$\frac{- 55}{4} + 4 (1) = 11$

No solution

$\frac{- 55}{4} + 4 (1) = 11$

No solution

Step 3.1.2

Move the negative in front of the fraction.

$- \frac{55}{4} + 4 (1) = 11$

No solution

Step 3.1.3

Multiply $4$ by $1$ .

$- \frac{55}{4} + 4 = 11$

No solution

$- \frac{55}{4} + 4 = 11$

No solution

Step 3.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{55}{4} + 4 \cdot \frac{4}{4} = 11$

No solution

Step 3.3

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

$- \frac{55}{4} + \frac{4 \cdot 4}{4} = 11$

No solution

Step 3.4

Combine the numerators over the common denominator.

$\frac{- 55 + 4 \cdot 4}{4} = 11$

No solution

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $4$ by $4$ .

$\frac{- 55 + 16}{4} = 11$

No solution

Step 3.5.2

Add $- 55$ and $16$ .

$\frac{- 39}{4} = 11$

No solution

$\frac{- 39}{4} = 11$

No solution

Step 3.6

Move the negative in front of the fraction.

$- \frac{39}{4} = 11$

No solution

No solution

Step 4

Since $- \frac{39}{4} \neq 11$ , there are no solutions.

No solution

Step 5

The ordered pair is not a solution to the system of equations.

$(\frac{5}{4}, 1)$ is not a solution

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$