Answered

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Q.6. The pair of equations [tex] x=0 [/tex] and [tex] x=-4 [/tex] has:

a) a unique solution
b) no solution
c) infinitely many solutions
d) only solution [tex] (0,0) [/tex]

Sagot :

GinnyAnswer
To determine the number of solutions to the pair of equations \( x = 0 \) and \( x = -4 \), let's analyze each equation one by one.

1. Equation 1: \( x = 0 \)
- This equation states that \( x \) must be 0.

2. Equation 2: \( x = -4 \)
- This equation states that \( x \) must be -4.

Now, for a solution to satisfy both equations simultaneously, the value of \( x \) must satisfy both \( x = 0 \) and \( x = -4 \) at the same time. However, this is not possible, because:

- If \( x \) is 0, it cannot be -4.
- If \( x \) is -4, it cannot be 0.

Therefore, there is no value of \( x \) that can satisfy both \( x = 0 \) and \( x = -4 \) simultaneously. As a result, the pair of equations \( x = 0 \) and \( x = -4 \) has no solution.

Hence, the correct answer is:
b) no solution
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