Solving Systems of Equations: Graphing and Substitution

Front

What is a system of equations?

Back

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

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

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

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the graphing method in solving systems of equations?

Back

It involves graphing both equations on the same coordinate plane and identifying their point of intersection.

Front

What is an ordered pair?

Back

A pair of numbers (x, y) that represent a point on a coordinate plane.

Front

What does it mean for an ordered pair to be a solution to a system of equations?

Back

It means that the ordered pair satisfies both equations in the system.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run.

Front

How do you find the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, found by setting x=0 in the equation.