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Select the correct answer. The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the y-variable, and what is the solution for this system? x + 3y = 42 2x − y = 14 A. Multiply the second equation by -3. The solution is x = 12, y = 9. B. Multiply the second equation by -2. The solution is x = 12, y = 10. C. Multiply the second equation by 2. The solution is x = 15, y = 9. D. Multiply the second equation by 3. The solution is x = 12, y = 10.



Answer :

TNAnushkalodha23

Answer:

x is 13 and y is 10

Step-by-step explanation:

Multiply the second equation by 3

sqdancefan

Answer:

 D. Multiply the second equation by 3. The solution is x = 12, y = 10.

Step-by-step explanation:

You want the multiplier for the elimination of the y-variable in the system of equations x +3y = 42; 2x -y = 14.

Multiplier

The coefficients of y are +3 and -1, so multiplying the second equation by 3 will make it the opposite of the former. Then their sum is zero, which is what you want when eliminating the y-variable.

Application

Multiplying the second equation by 3 and adding the first gives ...

  3(2x -y) +(x +3y) = 3(14) +(42)

  7x = 84 . . . . . . . . . simplify. Note the y-variable has been eliminated.

  x = 12 . . . . . . . . . divide by 7

  2(12) -y = 14 . . . . substitute for x in the second equation

  24 -14 = y = 10 . . . . add y-14

The solution is (x, y) = (12, 10).

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