Math 1 Benchmark 2 Review Part 3

Front

What does it mean when a system of two identical (overlapping) lines has infinite solutions?

Back

It means that every point on the line is a solution to the system, as the two lines are the same.

Front

How can you represent a situation with a system of equations?

Back

Identify the variables, write equations based on the relationships and constraints given in the problem.

Front

What is the general form of a linear equation in two variables?

Back

The general form is Ax + By = C, where A, B, and C are constants.

Front

What does the solution of a system of equations represent graphically?

Back

It represents the point(s) where the lines intersect on a graph.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines: parallel lines have no solutions, identical lines have infinite solutions, and intersecting lines have one solution.

Front

What is the significance of the coefficients in a system of equations?

Back

They represent the rate of change of the variables in relation to each other.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What does it mean if a system of equations has no solution?

Back

It means the lines are parallel and will never intersect.

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into the original equations to see if they hold true.