Two equivalent linear systems can have different solution sets.
Yes, it is possible for two equivalent linear systems to have different solution sets
Yes, it is possible for two equivalent linear systems to have different solution sets.
In mathematics, linear systems are a set of equations with multiple variables that are to be solved simultaneously. Two linear systems are considered equivalent if they have the same solution set, meaning that they represent the same relationship between the variables.
However, even though two linear systems may have the same coefficients and constants, they can still have different solution sets if they are represented by different forms or equations.
For example, consider the following two linear systems:
System 1:
2x + y = 4
3x – y = 2
System 2:
4x + 2y = 8
6x – 2y = 4
System 1 and System 2 have the same coefficients and constants, but they are represented in different forms. System 1 is represented in standard form, while System 2 is represented in slope-intercept form.
If we solve these two systems, we find that System 1 has a unique solution of x = 2 and y = 0, while System 2 has infinitely many solutions represented by the equation 2x + y = 4. This shows that two equivalent linear systems can indeed have different solution sets.
Therefore, it is important to be careful when comparing and solving linear systems as their forms or representations can affect the solution set.
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