25 m - 10 n = 75
6 m + 10 n = 18
---------------------- add
31 m = 93
etc
5m-2n=15---(i)
3m+5n=9---(ii)
3 answers
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
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
D =
|5 -2|
|3 5|
Dx =
|15 -2|
|9 5|
Dy =
|5 15|
|3 9|
x = Dx/D
y = Dy/D
|5 -2|
|3 5|
Dx =
|15 -2|
|9 5|
Dy =
|5 15|
|3 9|
x = Dx/D
y = Dy/D