Digits, Grade 8, Volume 1, Homework Helper

8-2: TEKS Practice

• 1. Without graphing, decide whether the system of equations has one solution, no solution, or infinitely many solutions.

y = 3x + 14

y = −3x + 14

• 2. Without graphing the equations, decide whether the system has one solution, no solution, or infinitely many solutions.

5y = x − 9

4x − 10y = 18

• 3. Does this system have one solution, no solution, or an infinite number of solutions?

3x + 2y = 7

27x + 18y = 5

• 4. Decide if the system of equations has one solution, no solution, or infinitely many solutions.

3x + 18y = 252

6x − 36y = 128

• 5. How many solutions does this system have?

x + 5y = 0

25y = −5x

• 6.

• a. Writing How many solutions does the system of equations have?

table with 2 rows and 2 columns , row1 column 1 , 8 x plus 10 y , column 2 equals 21 , row2 column 1 , y , column 2 equals negative , 4 fifths , x plus 24 , end table

• b. Write a situation you could model using this system of equations. Then interpret the number of solutions in the context of your situation.

• 7. Reasoning How many solutions are there for this system of equations?

y = 9x + 1

y = 7x + 1

• A. Exactly one solution, because the slopes are not equal.

• B. No solution, because the slopes are equal and the y-intercepts are not equal.

• C. No solution, because the y-intercepts are not equal.

• D. Exactly one solution, because the slopes are equal but the y-intercepts are not equal.

• E. Infinitely many solutions, because the slopes are equal and the y-intercepts are equal.

• 8. Mental Math By inspecting the equations, what can you determine about the solution(s) of this system?

y = 6x + 16

4y = 24x + 68

• A. The system has exactly one solution.

• B. The system has infinitely many solutions.

• C. The system has no solution.

• 9. Error Analysis Charlene says that this system of equations has infinitely many solutions.

13x + 4y = 33

26y + 8x = 66

• a. How many solutions does the system have?

• b. What error might Charlene have made?

• A. Charlene compared the slope in the first equation to the y-intercept in the second.

• B. Charlene found the y-intercept incorrectly.

• C. Charlene compared the y-intercept in the first equation to the slope in the second.

• D. Charlene found the slope incorrectly.

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