Linear inequalities in two variables (Algebra 1, Linear inequalities) – Mathplanet (2024)

FAQs

What is the answer to a linear inequality in two variables? ›

The solution for linear inequalities in two variables is an ordered pair that is true for the inequality statement. Let us say if Ax + By > C is a linear inequality where x and y are two variables, then an ordered pair (x, y) satisfying the statement will be the required solution.

Solving single linear inequalities follow pretty much the same process for solving linear equations. We will simplify both sides, get all the terms with the variable on one side and the numbers on the other side, and then multiply/divide both sides by the coefficient of the variable to get the solution.

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.

The symbol ≤ means less than or equal to. The symbol ≥ means greater than or equal to.

Inequality is the difference in social status, wealth, or opportunity between people or groups. People are concerned about social inequality. Synonyms: disparity, prejudice, difference, bias More Synonyms of inequality.

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.

Linear inequalities in one variable – 'x' where a ≠0: ax + b >0; ax + b ≤ 0. Linear inequalities in two variables – 'x' and 'y' where a ≠ 0 and b ≠ 0: ax + by < c; ax + by ≥ c.

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. Solving linear inequalities is the same as solving linear equations; the difference it holds is of inequality symbol.

How to solve a linear equation? ›

To solve linear equations graphically, first graph both equations in the same coordinate system and check for the intersection point in the graph. For example, take two equations as 2x + 3y = 9 and x – y = 3. Now, to plot the graph, consider x = {0. 1, 2, 3, 4} and solve for y.

Linear Inequations are two expressions where their values are compared by the inequality symbols such as <, >, ≤ or ≥. One variable linear equations and Inequations have only one solution or one root. Examples of one variable linear equations and inequations are x = 4, 2a + 3 = 9, 3x < 2 , 4y - 5 > 6.

When solving inequalities with variables on both sides of the inequality, first combine the variables into a single variable on the same side of the inequality. To isolate the variable, do the same order of operations on both sides of the inequality.

Linear inequalities in one variable – 'x' where a ≠0: ax + b >0; ax + b ≤ 0. Linear inequalities in two variables – 'x' and 'y' where a ≠ 0 and b ≠ 0: ax + by < c; ax + by ≥ c.