If y + 40x + 2 = 0, what is the value of xy?

Could someone please help me with the explanation.
Since both the equations are simplified to form:

4x+y =7

How do we get xy in this case?

1. We have two equation. Sufficient to find x and y values

Eliminate BCE

2. We have two equation. Sufficient to find x and y values

Hence, its D

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Statement 1 - solving the two equations x=-1/4 & y=8 hence xy=-2
Statement 2 - since it the same line hence the values of x & y will be the same as from statement 1. Hence answer is D

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\(y + 40x + 2 = 0\) --------- (i)

(1) \(16x = –4y + 28\)

\(4x = -y + 7\)

\(y + 4x = 7\) -------- (ii)

Subtracting (i) and (ii) we can find the value of \(x\) and \(y\). Hence we can find the value of \(xy\).

Hence I is Sufficient.

(2) \(13y = 91 – 52x\)

\(y = 7 - 4x\)

\(y + 4x = 7\) ---------- (iii)

Subtracting (i) and (iii) we can find the value of \(x\) and \(y\). Hence we can find the value of \(xy\).

Hence II is Sufficient.

Answer (D)...

What is the OA for the question

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Target question: What is the value of xy?

Given: y + 40x + 2 = 0
Rearrange to get: 40x + y = -2

IMPORTANT: We are given one linear equation. If we given a different linear equation, then we can be certain to solve the system of equations for x and y, which means we can determine the value of xy
So, we need only determine whether each statement provides a linear equation that is different from the given linear equation (40x + y = -2)

Statement 1: 16x = –4y + 28
Divide both sides by 4 to get: 4x = -y + 7
Add y to both sides: 4x + y = 7
This second linear equation is different from the given linear equation (40x + y = -2)
This means we COULD solve the system of equations for x and y, which means we COULD determine the value of xy
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 13y = 91 – 52x
Divide both sides by 13 to get: y = 7 - 4x
Add 4x to both sides: 4x + y = 7
This is the same equation that we have in statement 1.
So, if statement 1 is sufficient, we can also be certain that statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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