Systems of Equations & Inequalities 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.

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What does it mean for two lines to be coinciding?

Back

Coinciding lines are two lines that lie on top of each other, meaning they have infinitely many solutions.

Front

What is the graphical representation of parallel lines?

Back

Parallel lines are lines in a plane that never meet; they have the same slope but different y-intercepts.

Front

What is the solution to a system of equations represented by intersecting lines?

Back

The solution is the point where the two lines intersect, which represents the values of the variables that satisfy both equations.

Front

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

Back

A system has no solution if the lines are parallel, meaning they have the same slope but different y-intercepts.

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What is substitution in solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

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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

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

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How can you represent a system of equations graphically?

Back

You can represent a system of equations by graphing each equation on the same coordinate plane and finding the intersection points.

Front

What is the first step in solving a word problem using systems of equations?

Back

The first step is to define the variables that represent the unknowns in the problem.