Two systems of equations are shown below. The first equation in System B is the original equation in system A. The second equation in System B is the sum of that equation and a multiple of the second equation in System A. A. x + 3y = 11 → x + 3y = 11 5x - y = 17 → 15x - 3y = 51 15x = 62 B. x + 3y = 11 15x = 62 What is the solution to both systems A and B?

Question

Melody Davenport

Mathematics

21 February, 02:36

Two systems of equations are shown below. The first equation in System B is the original equation in system A. The second equation in System B is the sum of that equation and a multiple of the second equation in System A. A. x + 3y = 11 → x + 3y = 11 5x - y = 17 → 15x - 3y = 51 15x = 62 B. x + 3y = 11 15x = 62 What is the solution to both systems A and B?

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Francesca Shea · Answer 1

A.)

x + 3y = 11

5x - y = 17 ⇒ 15x - 3y = 51

15x = 62

B.) x + 3y = 11

15x = 62

x + 3y = 11

5x - y = 17

x = 11 - 3y

5x - y = 17

5 (11-3y) - y = 17

55 - 15y - y = 17

-16y = 17 - 55

-16y = - 38

y = - 38/-16

y = 2.375

x = 11 - 3y

x = 11 - 3 (2.375)

x = 11 - 7.125

x = 3.875

x = 3.875; y = 2.375

x + 3y = 11

3.875 + 3 (2.375) = 11

3.875 + 7.125 = 11

11 = 11