Question #305273

Consider the linear equation 2a + 3b = 4


Is (a; b) = (1; 1


2


) a solution to the equation? Motivate your answer.

1
Expert's answer
2022-03-07T08:12:03-0500

If (a,b)=(1,12),(a, b)=(1,\dfrac{1}{2}), then substitute


2(1)+3(12)=42(1) + 3(\dfrac{1}{2}) = 4

52=4,False\dfrac{5}{2}=4, False

Therefore (a,b)=(1,12)(a, b)=(1, \dfrac{1}{2}) is not a solution to the equation 2a+3b=1.2a+3b=1.


If (a,b)=(12,1),(a, b)=(\dfrac{1}{2}, 1), then substitute


2(12)+3(1)=42(\dfrac{1}{2}) + 3(1) = 4

4=4,True4=4, True

Therefore (a,b)=(12,1)(a, b)=(\dfrac{1}{2}, 1) is a solution to the equation 2a+3b=1.2a+3b=1.

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