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 two equations have a common solution, represented by the point where the lines cross.

Front

How can you solve a system of equations graphically?

Back

By plotting both equations on the same graph and identifying the point of intersection.

Front

What is the solution to the system of equations y = -x + 4 and y = 2x + 4?

Back

(0, 4)

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 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 you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is an infinite number of solutions in a system of equations?

Back

It occurs when the two equations represent the same line, meaning every point on the line is a solution.

Front

What is the graphical representation of the solution (3, 3)?

Back

It is the point where x = 3 and y = 3 on the coordinate plane.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines are parallel and do not intersect.