Understanding Two-Variable Linear Systems

What is the primary goal of the elimination method in solving linear systems?

• To eliminate one variable

• To find the slope of the line

• To graph the equations

• To multiply the equations

What happens when you multiply an equation by a constant in the elimination method?

• It changes the solution

• It makes the equation invalid

• It changes the slope

• It helps eliminate a variable

In the first system of equations, what is the value of y after elimination?

• 3

• 0

• -3

• 2

How can the solution to a system of equations be represented?

• As an ordered pair

• As a graph

• As a matrix

• As a single number

What is the graphical representation of a system with a single solution?

• Two perpendicular lines

• Two coincident lines

• Two intersecting lines

• Two parallel lines

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

• The lines intersect at one point

• The lines are parallel

• The lines overlap completely

• The lines form a triangle

What is the result when adding the equations in a system with no solution?

• x = 0

• 0 = 0

• 0 = 10

• x = y

What does it mean if a system of equations results in 0 = 0?

• There is one solution

• There are infinitely many solutions

• There is no solution

• The system is inconsistent

How can infinitely many solutions be described in terms of the lines?

• The lines form a right angle

• The lines intersect at one point

• The lines are parallel

• The lines are coincident

What is the relationship between the two equations in a system with infinitely many solutions?

• They have no common points

• They have different slopes

• They are perpendicular

• They are identical