What is the value of the x variable in the solution to the following system of equations?
3x + 2y = 8
2x + 3y = 2
Lets use 4:
3(4) + 2y = 8
12 + 2y = 8
12 + 2(-2) = 8
12 + -4 = 8
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2x + 3y = 2
2(4) + 3y = 2
8 + 3y = 2
8 + 3(-2) = 2
8 + (-6) = 2
So option A is true! (But remember that there can be more than one solution.)
Lets use -2:
3x + 2y = 8
3(-2) + 2y = 8
-6 + 2y = 8
-6 + 2(7) = 8
-6 + 14 = 8
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2x + 3y = 2
2(-2) + 3y = 2
-4 + 3y = 2
-4 + 3(2) = 2
-4 + 6 = 2
So option B is also true! (But again there can be more than one solution)
Answer:
So we have proved that there can be more than 1 solution for these set of equations. So the best answer is C: x can be any number as there are infinitely many solutions to this system.
