Which Ordered Pairs Make Both Inequalities True Select Two Options (2024)

FAQs

Which ordered pair makes both inequalities true: y 2x 3 y x 2? ›

y > -2x + 3 and y < x - 2. Summary: The ordered pair which makes both inequalities true are (3, 0).

The solution of a linear inequality in two variables like Ax + By > C is an ordered pair (x, y) that produces a true statement when the values of x and y are substituted into the inequality. The graph of an inequality in two variables is the set of points that represents all solutions to the inequality.

To see if an ordered pair is a solution to an inequality, plug it into the inequality and simplify. If you get a true statement, then the ordered pair is a solution to the inequality. If you get a false statement, then the ordered pair is not a solution.

Answer. The ordered pair solutions to the given system of inequalities, y > -2x and y <= 4, from the given choices are (0,-4) and (1,3). The given system of inequalities includes y > -2x and y <= 4.

A solution of a system of two linear equations is represented by an ordered pair (x,y). To determine if an ordered pair is a solution to a system of two equations, we substitute the values of the variables into each equation. If the ordered pair makes both equations true, it is a solution to the system.

Summary: If y = 2x - 3, the ordered pair (1, -1) lies on the graph.

Two ordered pairs are said to be equal if and only if the corresponding first elements are equal and the corresponding second elements are equal. For example: Consider two ordered pairs (a, b) and (c, d). They are equal if a = c and b = d, i.e., (a, b) = (c, d). Hence x = 8 and y = 6.

When solving an inequality: • you can add the same quantity to each side • you can subtract the same quantity from each side • you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed. So the solution is x > −1.

Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤ or ≥.

To solve inequalities, follow the same steps as with an equation. The order of operations is: parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right.

How to find ordered pair solutions? ›

To figure out if an ordered pair is a solution to an equation, you could perform a test. Identify the x-value in the ordered pair and plug it into the equation. When you simplify, if the y-value you get is the same as the y-value in the ordered pair, then that ordered pair is indeed a solution to the equation.

We say that a solution to an inequality 'satisfies' the inequality. This means when we substitute in the value (the number) for the variable, this value will make the inequality statement true.

Answer. y≤x and y≤−2, we need to check each option by substituting the values into the inequalities. Option B, (2,−4), is the only ordered pair that satisfies both inequalities.

To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Expert-Verified Answer

The first step in solving the inequality 2x + 3 ≥ 17 is "subtracting 3 from both the sides". The solution for the given inequality is x ≥ 7.

Multiplying or dividing both sides by a positive number leaves the inequality symbol unchanged. Rule 3. Multiplying or dividing both sides by a negative number reverses the inequality. This means < changes to >, and vice versa.

To solve a two-step inequality, undo the addition or subtraction first, using inverse operations , and then undo the multiplication or division. The inverse operation of addition is subtraction and vice versa. Similarly, the inverse operation of multiplication is division and vice versa.

If you add the same number to both sides of an inequality, the inequality remains true. If you subtract the same number from both sides of the inequality, the inequality remains true. If you multiply or divide both sides of an inequality by the same positive number, the inequality remains true.