Question

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Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added together, the x term is eliminated?

1/5x + 3/4y = 9

2/3x - 5/6y = 8
A: –10 times the first equation and 3 times the second equation
B: 10 times the first equation and 3 times the second equation
C: –3 times the first equation and 5 times the second equation
D: 3 times the first equation and 5 times the second equation



The multipliers of this system of equations have been determined to create opposite terms of the x-variable.

12(-1/6x - 2/3y = -5 )--------> -2x-8y=-60
5(2/5x + 1/5y = -9)----------> 2x+y=-45
What is the value of y?
A: –30
B:–15
C: 15
D: 30



Examine the system of equations. Which is an equivalent form of the first equation that when added to the second equation eliminates the y terms?

-5x + 3/4y = 12
8x + 12y = 11

A: 10x – 12y = –192
B:–10x + 12y = 192
C: 5x – 12y = 96
D: –5x + 12y = 96

Answer 1

Answer:

1. A: –10 times the first equation and 3 times the second equation
2. C: 15
3. none of the choices shown. Should be 80x -12y = -192

Step-by-step explanation:

1. The multiplier for the first equation can be found by the ratio ...

  -(second equation x-coefficient)/(first equation x-coefficient)

  = (-2/3)/(1/5) = -10/3

This tells you that multiplying the first equation by -10 and the second equation by 3 will make the x-terms cancel. Matches selection A.

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2. Adding the two equations shown gives ...

  (-2x -8y) +(2x +y) = (-60) +(-45)

  -7y = -105

  y = -105/-7 = 15 . . . . matches selection C.

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3. Using the rule shown in question 1, the multiplier for the first equation will be ...

  -(second equation y-coefficient)/(first equation y-coefficient)

  -12/(3/4) = -16

Multiplying the first equation by -16 gives ...

  -16(-5x +3/4y) = -16(12)

  80x -12y = -192 . . . . no matching answer choice

(Sometimes, the problems have errors in their answers. This is one of those times. Choice A will probably be graded as correct, even though it is not.)

Answer 2

Answer:

A.  10x – 12y = –192

Step-by-step explanation:

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