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.