Unit #5 Review (System of Equations & Inequalities)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

What does it mean for two lines to be parallel in a system of equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is less than, greater than, less than or equal to, or greater than or equal to the other.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Shade the region that satisfies the inequality.

Front

What does it mean for a solution to a system of inequalities?

Back

A solution to a system of inequalities is any point that satisfies all inequalities in the system, typically represented by the shaded region on a graph.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

What is the slope-intercept form of a linear equation?

Back

Front

How do you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into each equation. If the equations are satisfied, the point is a solution.