Question

Find an integral solution to the equation 4x+11y=−3.

A) x=2,y=−1
B) x=−2,y=1
C) x=−5,y=1
D) x=5,y=−1

Answer 1

After substituting each pair of integral values into the given linear equation 4x+11y=-3, only Option A (x=2, y=-1) satisfies the equation.

Step-by-step explanation:

The equation given is 4x+11y=-3, which we are told is linear, and we need to find an integral solution among the provided options. Our task is to substitute each pair of values (x,y) back into the equation and see if the resulting left-hand side equals the right-hand side, which is -3.

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• Option A: For x=2 and y=-1, the equation becomes 4(2)+11(-1) = 8 - 11 = -3, which is true.
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• Option B: For x=-2 and y=1, the equation becomes 4(-2)+11(1) = -8 + 11 = 3, which does not equal -3.
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• Option C: For x=-5 and y=1, the equation becomes 4(-5)+11(1) = -20 + 11 = -9, which does not equal -3.
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• Option D: For x=5 and y=-1, the equation becomes 4(5)+11(-1) = 20 - 11 = 9, which does not equal -3.

After checking each option, we see that only Option A provides a solution where the resulting value matches the right-hand side of the equation.