Question

5m-2n=15---(i)
3m+5n=9---(ii)

Answer 1

25 m - 10 n = 75
6 m + 10 n = 18
---------------------- add
31 m = 93
etc

Answer 2

There are several ways to solve that.

For example:

5 m - 2 n = 15

Multiply both sides by 3

15 m - 6 n = 45


3 m + 5 n = 9

Multiply both sides by 5

15 m + 25 n = 45


15 m - 6 n = 45
-
15 m + 25 n = 45
______________
15 m - 15 m - 6 n - 25 n = 45 - 45

- 31 n = 0

n = 0

Replace this in equation:

5 m - 2 n =15

5 m - 2 ∙ 0 =15

5 m = 15

m = 15 / 5

m = 3


OR

5 m - 2 n = 15

Add 2 n to both sides

5 m = 15 + 2 n

m = ( 15 + 2 n ) / 5

Put this value in equation:

3 m + 5 n = 9

3 ∙ ( 15 + 2 n ) / 5 + 5 n = 9

( 45 + 6 n ) / 5 + 5 n = 9

45 / 5 + 6 n / 5 + 5 n = 9

9 + 6 n / 5 + 5 n = 9

9 + 6 n / 5 + 5 n / 5 = 9

9 + 11 n / 5 = 9

Subtract 9 to both sides

11 / 5 n = 0

n = 0

Substitute n = 0 in equation:

5 m - 2 n = 15

5 m - 2 ∙ 0 = 15

5 m = 15

m = 15 / 5

m = 3


OR

5 m - 2 n = 15
-
3 m + 5 n = 9
___________

5 m - 3 m - 2 n - 5 n = 15 - 9

2 m - 7 n = 6

Add 7 n to both sides

2 m = 6 + 7 n

m = ( 6 + 7 n ) / 2

Put this value in equation:

3 m + 5 n = 9

Put this value in equation:

3 ∙ ( 6 + 7 n ) / 2 + 5 n = 9

( 3 ∙ 6 + 3 ∙ 7 n ) / 2 + 5 n = 9

( 18 + 21 n ) / 2 + 5 n = 9

18 / 2 + 21 n / 2 + 5 n = 9

9 + 21 n / 2 + 10 n / 2 = 9

9 + 31 n / 2 = 9

Subtract 9 to both sides

31 / 2 n = 0

n = 0

Substitute n = 0 in equation:

5 m - 2 n = 15

5 m - 2 ∙ 0 = 15

5 m = 15

m = 15 / 5

m = 3

Answer 3

D =
|5 -2|
|3 5|

Dx =
|15 -2|
|9 5|

Dy =
|5 15|
|3 9|

x = Dx/D
y = Dy/D