Solving Systems of Equations

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 if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point, which is the solution to the system.

Front

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

Back

The lines coincide, meaning they are the same line and intersect at every point on the line.

Front

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

Back

By graphing the equations and observing the intersection points of the lines.

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 is the graphical method of solving systems of equations?

Back

Plotting the equations on a graph and finding the point(s) where they intersect.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where all equations are satisfied.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.