Determining Solutions to Linear Equation Systems

What are the possible types of solutions for a system of linear equations?

• One solution, two solutions, or infinitely many solutions

• One solution, two solutions, or no solution

• One solution, no solution, or infinitely many solutions

• No solution, two solutions, or infinitely many solutions

What does it mean graphically if two lines intersect at one point?

• The system has no solution

• The system has one solution

• The system has infinitely many solutions

• The lines are parallel

If two lines are parallel, what type of solution does the system have?

• One solution

• No solution

• Two solutions

• Infinitely many solutions

When solving algebraically, what does it mean if you end up with a false numerical statement like 7 ≠ 4?

• The system has one solution

• The system has two solutions

• The system has infinitely many solutions

• The system has no solution

What does it mean if you solve algebraically and end up with a true statement like 14 = 14?

• The system has two solutions

• The system has no solution

• The system has one solution

• The system has infinitely many solutions

What is the first step in solving a system using the substitution method?

• Solve one equation for one variable

• Graph the equations

• Compare slopes and y-intercepts

• Eliminate one variable

How can you determine the type of solution by comparing slopes and y-intercepts?

• Same slopes and same y-intercepts mean no solution

• Same slopes and different y-intercepts mean one solution

• Different slopes mean no solution

• Different slopes mean one solution

What type of solution does a system have if the lines have the same slope but different y-intercepts?

• Two solutions

• Infinitely many solutions

• No solution

• One solution

If two lines have different slopes, what type of solution does the system have?

• Two solutions

• No solution

• One solution

• Infinitely many solutions

What is the solution to the system if the lines are coinciding?

• Infinitely many solutions

• No solution

• One solution

• Two solutions