Algebra I Final 2024 Review

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

To graph y < -x + 3, first graph the line y = -x + 3 as a dashed line (indicating that points on the line are not included). Then shade below the line to represent all points where y is less than -x + 3.

The inequality y > x - 1 represents the region above the line y = x - 1. The line is dashed, indicating that points on the line are not included in the solution.

To find the width, divide the area by the length. If the area is $$8x^2 + 6x - 9$$ and the length is $$2x + 3$$ , the width is $$\frac{{8x^2 + 6x - 9}}{{2x + 3}} = 4x - 3$$ .

The standard form of a linear inequality is expressed as Ax + By ≤ C or Ax + By ≥ C, where A, B, and C are constants.

Identify the variables, determine the relationship between them, and express the condition as an inequality. For example, selling hot chocolate for $1 and apple cider for $2 to make at least $240 can be written as $$x + 2y ≥ 240$$ .

The solution to the system is (-5, 1). This means x = -5 and y = 1 satisfy both equations.

A system of equations is consistent if there is at least one solution (the lines intersect at one point or are the same line).

A dashed line indicates that points on the line are not included in the solution (for < or >), while a solid line indicates that points on the line are included (for ≤ or ≥).

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.