Solving Systems of Equations by Graphing

What does a system of equations consist of?

• Equations without any variables

• Two or more equations with the same variables

• Only one equation

• Different equations with different variables

How can the solution of a system of equations be found?

• Only graphically

• Only algebraically

• Using calculus methods

• Either graphically or algebraically

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

• They intersect at infinitely many points

• They will never intersect

• They are not part of a system of equations

• They intersect at one point

What does an infinite number of solutions in a system of equations indicate about the lines?

• The lines intersect at multiple points

• The lines are the same

• The lines are perpendicular

• The lines are parallel

What is the graphical representation of an equation in slope-intercept form?

• b = y - mx

• mx - b = y

• y = mx + b

• x = my + b

What is the first step in solving systems of equations by graphing?

• Identify the type of lines

• Rewrite the equations in slope-intercept form

• Graph the equations

• Calculate the intersection point

In the context of graphing, what does the 'slope' indicate?

• The number of solutions in the system

• The direction and steepness of the line

• The intercept on the y-axis

• The point where lines intersect

What is the result when the graph of two equations in a system cross at exactly one point?

• Cannot be determined

• Infinite solutions

• No solution

• One solution

How do you graph a line if you know the slope and y-intercept?

• Start at the y-intercept and apply the slope

• Start at the origin and follow the slope

• Only plot the y-intercept

• Plot points randomly and connect them

What does the equation 'x = -2' represent on a graph?

• A vertical line through -2 on the x-axis

• A horizontal line through -2 on the y-axis

• An undefined line

• A diagonal line passing through -2 on both axes