Solve these systems of equations Using the elimination method.

a). 3x + y = 13 b) 6x - y = 14

x - 5y = 15 2x + y = 12

c) 3x - 4y = 22

2x + 5y = 7

A). 3x + y = 13

x - 5y = 15

multiplier equation 1 by 5

15x+5y=65

DSA

15x+5y=65

x - 5y = 15

remaini ng

16x=80

x=5

5-5y=15

-5y=15-5

-5y=10

y = 10 : - 5

y=-2

x, y

5,-2

A. 3x + y = 13 → 15x + 5y = 65

x - 5y = 15 → x - 5y = 15

16x = 80

16 16

x = 5

x - 5y = 15

5 - 5y = 15

- 5 - 5

-5y = 10

-5 - 5

y = - 2

(x, y) = (5, - 2)

b. 6x - y = 14

2x + y = 12

8x = 26

8 8

x = 3¹/₄

6x - y = 14

6 (3¹/₄) - y = 14

19¹/₂ - y = 14

- 19¹/₂ - 19¹/₂

-y = - 5¹/₂

-1 - 1

y = 5¹/₂

(x, y) = (3¹/₄, 5¹/₂)

c. 3x - 4y = 22 → 15x - 20y = 110

2x + 5y = 7 → 8x + 20y = 28

23x = 138

23 23

x = 6

3x - 4y = 22

3 (6) - 4y = 22

18 - 4y = 22

- 18 - 18

-4y = 4

-4 - 4

y = - 1

(x, y) = (6, - 1)