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equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller
and 1. How many solutions are possible for this situation?
Infinitely many solutions exist because the two situations describe the same line.
Exactly one solution exists because the situation describes two lines that have different slopes and different y-
intercepts.
No solutions exist because the situation describes two lines that have the same slope and different y-intercepts
Exactly one solution exists because the situation describes two lines with different slopes and the same y-
intercept.



Answer :

GinnyAnswer
Let's break down the problem step by step:

We are given two statements about two numbers, a larger number [tex]\( L \)[/tex] and a smaller number [tex]\( S \)[/tex]:

1. The larger number is equal to twice the smaller number plus 3:
[tex]\[ L = 2S + 3 \][/tex]

2. The larger number is equal to twice the sum of the smaller number and 1:
[tex]\[ L = 2(S + 1) \][/tex]

Let's express the second equation in terms of [tex]\( S \)[/tex]:
[tex]\[ L = 2(S + 1) \][/tex]
Expanding the right-hand side, we get:
[tex]\[ L = 2S + 2 \][/tex]

Now we have two equations:
1. [tex]\( L = 2S + 3 \)[/tex]
2. [tex]\( L = 2S + 2 \)[/tex]

If we equate these expressions for [tex]\( L \)[/tex], we get:
[tex]\[ 2S + 3 = 2S + 2 \][/tex]

Subtract [tex]\( 2S \)[/tex] from both sides:
[tex]\[ 3 = 2 \][/tex]

This is a contradiction, as 3 does not equal 2. Therefore, these two equations describe two lines that have the same slope but different y-intercepts.

Thus, no solutions exist because the situation describes two lines that have the same slope and different y-intercepts.

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