Special Systems of Linear Equations

• Infinite solutions

Problem #22

Precision: Find the values of a and b so the system shown has the solution (2, 3).

Does the system have any other solutions? Explain.

• yes, both equations are the same.

• no, the equations are different.

Let x and y be two numbers. Find the solution of the puzzle.

• one solution

• no solution

• infinitely many solutions

Without graphing, determine whether the system of linear equations has one solution, infinitely many solutions, or no solution.

• one solution

• no solution

• infinitely many solutions

Without graphing, determine whether the system of linear equations has one solution, infinitely many solutions, or no solution. Explain your reasoning.

• The lines have the same slope and different

  y-intercepts.

• The lines have different slopes.

• The lines have different slopes and the same y-intercept.

Problem #14

ERROR ANALYSIS: Correct the error in solving the system of linear equations.

• one solution

• no solution

• infinitely many solutions

Problem #14

ERROR ANALYSIS: Describe the error in solving the system of linear equations.

• The lines have different y-intercepts, so the lines are parallel.

• The lines have different slopes.

• The lines have the same slope and the same y-intercept.

REASONING: One equation in a system of linear equations has a slope of − 3. The other equation has a slope of 4. How many solutions does the system have? Explain.

• The lines have different y-intercepts, so the lines are parallel.

• The lines have different slopes, they will intersect in one point.

MONEY: You and a friend both work two different jobs. The system of linear equations represents the total earnings for x hours worked at the first job and y hours worked at the second job. Your friend earns twice as much as you.

One week, both of you work 4 hours at the first job. How many hours do you and your friend work at the second job?

_____ hours

Mathematical Equivalence

ON

Problem #18 b

MONEY: You and a friend both work two different jobs. The system of linear equations represents the total earnings for x hours worked at the first job and y hours worked at the second job. Your friend earns twice as much as you.

b. Both of you work the same number of hours at the second job. Compare the number of hours each of you works at the first job.

• You both work a different number of hours at the first job.

• You both work the same number of hours at the first job.

• One of you worked the first job, while the other worked the second job.