Answer:
a. To write a system of equations with exactly 1 solution, we need to find two equations that intersect at a single point. We can choose any two of the given equations and solve for x and y to find their point of intersection:
From y = 4x + 2 and y = 9x + 2, we have:
4x + 2 = 9x + 2
-5x = 0
x = 0
Substituting x = 0 into either equation gives us y = 2. Therefore, the system of equations with exactly 1 solution is:
y = 4x + 2
y = 9x + 2
b. To write a system of equations with exactly no solutions, we need to find two equations that are parallel and never intersect. We can choose any two of the given equations that have different slopes (since parallel lines have the same slope) and different y-intercepts.
From y = 4x + 2 and y = 9x + 2, we see that they have the same y-intercept (2), so they cannot be parallel.
However, if we choose y = 4x + 2 and y = 9x + 5, we have:
4x + 2 = 9x + 5
-5x = 3
x = -3/5
Substituting x = -3/5 into either equation gives us y = -8/5. Therefore, the system of equations with exactly no solutions is:
y = 4x + 2
y = 9x + 5
Step-by-step explanation: have a good day
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