6x + 7y = 28 2x + 2y = 10The solution to the given system of equations is (x, y). What is the value of y ?
Correct answer: A. -2
- A. -2
- B. 7
- C. 14
- D. 18
Explanation
First, let's rearrange the second equation to solve for y. Multiply both sides by 2 to get:4x + 4y = 20Now we can eliminate x by subtracting the second equation from the first equation:(6x + 7y) - (4x + 4y) = 28 - 202x + 3y = 8Subtracting corresponding terms gives:2x - 4x + 3y - 4y = 8 - 20- 2x - y = - 12Now solve for y:- y = - 12 + 2xy = 12 - 2xWe can substitute this value of y into the second equation:2x + 2(12 - 2x) = 102x + 24 - 4x = 10- 2x + 24 = 10- 2x = - 14x = 7Now substitute the value of x into the equation we found for y:y = 12 - 2(7)y = 12 - 14 y = -2So the solution to the system of equations is (x, y) = (7, -2). Therefore, the value of y is -2.
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