13]

a]

x + y = 1

4x - y = 9

--------------- +

5x = 10

x = 10/5

x = 2

x + y = 1

2 + y = 1

y = 1 - 2

y = -1

so the value of x and y is {(2, -1)}

b]

-x - y = 12

x = -12 - y

3x - 4 = 2y

3(-12 - y) - 4 = 2y

-36 - 3y - 4 = 2y

-40 - 3y = 2y

-40 = 2y + 3y

-40 = 5y

y = -40/5

y = -8

x = -12 - y

x = -12 - (-8)

x = -12 + 8

x = -4

so the value of x and y is {(-4 , -8)}

c]

8x = 3y + 19

x = (3y + 19)/8

2x - 5y = 11

2[(3y + 19)/8] - 5y = 11

(3y + 19)/4 - 20y/4 = 11

(3y + 19 - 20y)/4 = 11

(-17y + 19)/4 = 11

-17y + 19 = 11 × 4

-17y + 19 = 44

-17y = 44 - 19

-17y = 25

y = 25/(-17)

y = -25/17

x = (3y + 19)/8

x = (3(-25/7) + 19)/8

x = (-75/7 + 133/7)/8

x = (58/7) × 1/8

x = 58/56

so the value of x and y is {(58/56 , -25/17)}

d]

(2x + y)/6 = 2/3 ----> (× 6)

2x + y = 4

y = 4 - 2x

(x - 2y)/4 = 1/2 ----> (× 4)

x - 2y = 2

x - 2(4 - 2x) = 2

x - 8 + 4x = 2

5x - 8 = 2

5x = 2 + 8

5x = 10

x = 10/5

x = 2

y = 4 - 2x

y = 4 - 2(2)

y = 4 - 4

y = 0

so the value of x and y is {(2 , 0)}

e]

(4x)/3 + (3y)/2 = 4 ---> (× 6)

8x + 9y = 24

(-y)/4 - (3x)/2 = 7 -----> (× 36)

-9y - 54x = 252

-54x - 9y = 252

8x + 9y = 24

-54x - 9y = 252

------------------------ +

-46x = 276

x = 276/(-46)

x = -6

8x + 9y = 24

8(-6) + 9y = 24

-48 + 9y = 24

9y = 24 + 48

9y = 72

y = 72/9

y = 8

so the value of x and y is {(-6 , 8)}