Systems of Equations & Inequalities Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations by elimination?

Back

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

Front

What is the graphical representation of a system of equations?

Back

The solution is the point where the graphs of the equations intersect.

Front

What are infinitely many solutions in a system of equations?

Back

This occurs when the equations represent the same line, meaning every point on the line is a solution.

Front

What is the difference between parallel lines and intersecting lines in terms of solutions?

Back

Parallel lines have no solutions (they never intersect), while intersecting lines have exactly one solution (the point of intersection).

Front

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

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

What is the substitution method for solving systems of equations?

Back

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

Front

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

Back

The coefficients determine the slope and position of the lines represented by the equations.

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.

Front

What is the formula for finding the intersection point of two lines given by equations?

Back

Solve the system of equations simultaneously to find the values of the variables at the intersection.