Solving Systems of Equations

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 two lines to intersect on a graph?

Back

It means that the solution to the system of equations is the point where the two lines meet.

Front

How can you find the solution to 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 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, making it easier to solve for the other.

Front

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

Back

It means there is no solution, as the lines never intersect.

Front

What is the graphical representation of the solution to a system of equations?

Back

The point (x, y) where the two lines intersect.

Front

How do you determine if a point is a solution to a system of equations?

Back

By substituting the point's coordinates into both equations and checking if they hold true.

Front

What is the meaning of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes (rise over run).

Front

What is the y-intercept in a linear equation?

Back

The y-coordinate where the line crosses the y-axis (when x=0).