Solving Systems of Equations (ALG 1)

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 one solution?

Back

The lines representing the equations intersect at exactly one point.

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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 infinitely many solutions?

Back

The lines representing the equations are the same line, overlapping completely.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

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.

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What is the graphical method for solving systems of equations?

Back

A method that involves graphing the equations and finding the point(s) of intersection.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

How do you find the slope from an equation in slope-intercept form?

Back

The slope is the coefficient of x in the equation y = mx + b.