Question

What are the answers for these 11, 14, 15, 16 and 20.

Answer 1

11. (x, y) -> (7, -3)

14. (x, y) -> (-3, -2)

15. (x, y) -> (-3, 2)

16. (x, y) -> (7,6)

20.(x, y) -> (4, 1)

Explanation:

11.

x + 3y = 1

-3x -3y = -15

-2x = -14

/-2 /-2

x = 7

x + 3y = 1

7 + 3y = 1

-7 -7

3y = -6

/3 /3

y = -2

(x, y) -> (7, -3)

14.

-3x + 3y = 3

-5x + y = 13

-5x + y = 13

+5x +5x

y = 5x + 13

-3x + 3(5x + 13) = 3

-3x + 15x + 39 = 3

12x + 39 = 3

- 39 -39

12x = -36

/12 /12

x = -3

Now, we solve for y:

-5x + y = 13

-5(-3) + y = 13

15 + y = 13

-15 -15

y = -2

(x, y) -> (-3, -2)

15.

6x + 6y = -6

5x + y = -13

5x + y = -13

-5x -5x

y = -5x - 13

6x + 6y = -6

6x + 6(-5x - 13) = -6

6x -30x - 78 = -6

-24x - 78 = -6

+ 78 + 78

-24x = 72

/-24 /-24

x = -3

Now, we solve for y:

6x + 6y = -6

6x + 6y = -6

6(-3) + 6y = -6

-18 + 6y = -6

+18 +18

6y = 12

/6 /6

y = 2

(x, y) -> (-3, 2)

16.

2x + y = 20

6x - 5y = 12

2x + y = 20

-2x -2x

y = -2x + 20

6x - 5y = 12

6x - 5(-2x + 20) = 12

6x + 10x - 100 = 12

16x - 100 = 12

+ 100 +100

16x = 112

/16 /16

x = 7

Now, we solve for y:

2x + y = 20

2(7) + y = 20

14 + y = 20

-14 -14

y = 6

(x, y) -> (7,6)

20.

-2x - y = -9

5x - 2y = 18

-2x - y = -9

+2x +2x

-y = 2x - 9

/-1 /-1

y = -2x + 9

5x -2y = 18

5x - 2(-2x + 9) = 18

5x + 4x - 18 = 18

9x - 18 = 18

+ 18 + 18

9x = 36

/9 /9

x = 4

Now, we solve for y:

-2(4) - y = -9

-8 - y = -9

+ 8 +8

-y = -1

/-1 /-1

y = 1

(x, y) -> (4, 1)

Hope this helps!