85.5k views
5 votes
PLEASE HELP! The image is below

PLEASE HELP! The image is below-example-1

1 Answer

2 votes

9514 1404 393

Answer:

  • (3)
  • (1)
  • 0x -1y = -9

Explanation:

The general approach here is to choose a variable you want to eliminate, identify the coefficients of it, and use those to multiply the equations so adding the products will eliminate the variable.

Here, the coefficients of x are -1 and -3; the coefficients of y are 2 and 5. We often like to choose the set of coefficients that includes 1 or where the coefficients are related by an integer factor. These criteria suggest that we should use the coefficients -1 and -3. One of our multipliers must be the opposite of one of these coefficients. So, we choose for them to be -3 and +1.

That is, multiplying the first equation by -3 will make the x-coefficient be 3; multiplying the second equation by 1 will make the x-coefficient be -3. Adding these equations will then eliminate x terms.

(-3)(-x +2y = 12)

+ (1)(-3x +5y =27)

gives (3x -6y) +(-3x +5y) = -36 +27

which simplifies to the sum ...

0x -1y = -9

__

Dividing by the coefficient of y, we find y = 9. Substituting into the first equation, we have ...

-x +2(9) = 12)

x = 18-12 = 6

The solution is (x, y) = (6, 9).

User Eloims
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories