Systems of Linear Equations and Inequalities Review

Front

What are the methods to solve systems of linear equations?

Back

The methods include graphing, substitution, and elimination.

Front

How do you find the solution to a system of equations by graphing?

Back

Plot the equations on a graph and identify the point where they intersect.

Front

What does the solution (3, 3) represent in a system of equations?

Back

It represents the point where the two equations intersect, meaning x=3 and y=3.

Front

What is the significance of the graph in solving inequalities?

Back

The graph visually represents the solution set of the inequality.

Front

How do you determine which graph corresponds to a given inequality?

Back

Analyze the inequality to identify the boundary line and shading direction.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for a variable and substituting that expression into the other equation.

Front

Given the equations 7x + y = -20 and y = 3x + 10, how do you solve by substitution?

Back

Substitute y from the second equation into the first equation to find x, then back-substitute to find y.

Front

What does the solution (-3, 1) indicate in the context of a system of equations?

Back

It indicates the values of x and y that satisfy both equations in the system.

Front

What is an inequality in the context of linear equations?

Back

An inequality is a mathematical statement that compares two expressions, indicating that one is greater than, less than, or not equal to the other.

Front

How can you graph a linear inequality?

Back

Graph the corresponding linear equation as a boundary line, then shade the appropriate region based on the inequality.