Algebra Examples

$5 x - y > - 2$ , $(- 3, - 4)$

Step 1

Insert the values of $x = - 3$ and $y = - 4$ into the equation to find if the ordered pair is a solution.

$5 (- 3) - (- 4) > - 2$

Step 2

Simplify $5 (- 3) - (- 4)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $5$ by $- 3$ .

$- 15 - (- 4) > - 2$

Step 2.1.2

Multiply $- 1$ by $- 4$ .

$- 15 + 4 > - 2$

Step 2.2

Add $- 15$ and $4$ .

$- 11 > - 2$

Step 3

The inequality is never true.

No solution

Step 4

Identify the leading coefficient.

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Step 4.1

The leading term in a polynomial is the term with the highest degree.

$- 9$

Step 4.2

The leading coefficient in a polynomial is the coefficient of the leading term.

$- 9$

Step 5

Since there are no real x-intercepts and the leading coefficient is negative, the parabola opens down and $- 9$ is always less than $0$ .

No solution

Step 6

Since the equation is not true when the values are used, the ordered pair is not a solution.

The ordered pair is not a solution to the equation.