Solving Special Systems of Linear Equations

Solve the system.

• No solutions

• Infinitely many solutions

• Cannot be determined.

Problem #22

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

• a = 2

  b = 4

• a = 2

  b = 2

• a = -2

  b = -4

• a = 2

  b = -2

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.

• 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?

• one solution

• no solution

• infinitely many solutions

Problem #16

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.

Problem a

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.

a. 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