System of Equations Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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What does it mean for a system of equations to have a solution?

Back

It means there is at least one set of values for the variables that satisfies all equations in the system.

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What is the graphical representation of a system of equations?

Back

The solution is represented by the point(s) where the graphs of the equations intersect.

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What does it mean if two lines are parallel in a system of equations?

Back

It means the system has no solution because the lines never intersect.

Front

How can you solve a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point of intersection.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted 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 the equations represent the same line, and every point on that line is a solution.

Front

What is an example of a system of equations with no solution?

Back

y = 2x + 3 and y = 2x - 1 (parallel lines).

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How do you check if a solution is correct for a system of equations?

Back

Substitute the solution values into each equation to see if they hold true.