System 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 for a system of equations to have one solution?

Back

It means the graphs of the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the equations represent the same line, overlapping each other.

Front

What does it mean for a system of equations to have no solution?

Back

It means the graphs of the equations are parallel and never intersect.

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

By analyzing the slopes and y-intercepts of the equations.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then 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.

Front

What is the graphical method for solving systems of equations?

Back

A method where the equations are graphed, and the solution is the point of intersection.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the solution to a system of equations graphically?

Back

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