Special Systems of Linear Equations Slope and Intercept

• 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

Shari takes violin lessons. The equation 288x – 4y = -192 relates y, the total cost of the lessons, and x, the number of lessons. Shari incorrectly states that the slope of the line is 288. Why did Shari think that 288 was the slope? Choose one option from each drop-down menu to answer the question.

• write the equation in slope-intercept form.

• coefficient of x

• coefficient of y

• divide -192 by 4

• divide 288 by -4

• -48

• 72

• -72

• 48

• constant term

Shari takes violin lessons. The equation 288x – 4y = -192 relates y, the total cost of the lessons, and x, the number of lessons. Shari incorrectly states that the slope of the line is 288. Why did Shari think that 288 was the slope? Choose one option from each drop-down menu to answer the question. Shari thought that the ​ (a)   was the slope. She forgot to ​ (b)   . The correct slope is ​ ​ (c)   .

• write the equation in slope-intercept form.

• coefficient of x

• coefficient of y

• divide -192 by 4

• divide 288 by -4

• -48

• 72

• -72

• 48

• constant term

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 #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

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

• one solution

• no solution

• infinitely many solutions