Unit 6: Systems of Equations Test Review

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.

Front

What does it mean for two lines to be coinciding?

Back

Two lines are coinciding if they lie on top of each other, meaning they have infinitely many solutions.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they never intersect, meaning they have no solutions.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, write equations based on the relationships described, and ensure the equations represent the same situation.

Front

What is the graphical method for solving a system of equations?

Back

The graphical method involves plotting both equations on a graph and identifying the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and 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.

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, which means they never intersect.

Front

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

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.

Front

How can you find the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines, you can determine if there are no solutions, one solution, or infinitely many solutions.