Question

5m - 3n = 19 ; m - 6n = -7

Answer 1

5m - 3n = 19   (equation 1)

m - 6n = -7   (equation 2)

Substitution Method:

From equation 2,

m - 6n = -7

m = 6n - 7   (equation 3)

Substitute equation 3 into equation 1,

5 (6n - 7) - 3n = 19

30n - 35 -3n = 19

27n - 35 = 19

27n = 19 + 35

n = 2

Substitute n = 2 into equation 3,

m = 6 (2) - 7

m = 5

Hence, n is 2 and m is 5.

Answer 2

Answer:

5m – 3n = 19 .....(I)

m – 6n = –7 .....(II)

Multiplying (I) with 2 we get

10m – 6n = 38 .....(III)

m – 6n = –7 .....(IV)

Subtracting (IV) from (III) we get

10m-m-6n-(-6n)=38-(-7)

⇒9m=45

⇒m=45/9

=5

Putting the value of m = 5 in (II) we get

5-6n=-7⇒-6n=-7-5

⇒-6n=-12

⇒n=-12/-6

=2

Thus, (m, n) = (5, 2).