Understanding Two-Variable Linear Systems

What is the primary method discussed for solving two-variable linear systems?

• Substitution method

• Matrix method

• Graphical method

• Elimination method

In the elimination method, what is the goal when adding equations?

• To solve for both variables simultaneously

• To determine the y-intercept

• To eliminate one of the variables

• To find the slope of the line

What is the solution to the system of equations: x - 2y = 8 and 1/2x + y = -2?

• (0, 0)

• (1, -4)

• (3, -2)

• (2, -3)

What should you do if you want to find the x-value after finding the y-value in a system of equations?

• Substitute the y-value into one of the original equations

• Guess the x-value

• Use the elimination method again

• Graph the equations

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

• The lines intersect at one point

• The lines are parallel and never intersect

• The lines coincide

• The lines form a right angle

What is the result when adding the equations -3x + 6y = 9 and 3x - 6y = 1?

• 0 = 10

• 0 = 0

• 9 = 9

• 1 = 1

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

• There is a unique solution

• There is no solution

• The system is inconsistent

• There are infinitely many solutions

How can you describe the solution set for a system with infinitely many solutions?

• A set of intersecting lines

• A set of all ordered pairs on a line

• A set of parallel lines

• A single point

What is the relationship between the two equations x + y = 1 and 2x + 2y = 2?

• They are the same line

• They are parallel lines

• They form a right angle

• They intersect at one point

What is the graphical interpretation of a system with infinitely many solutions?

• The lines form a triangle

• The lines coincide

• The lines are parallel

• The lines intersect at one point