Question

Solve the simultaneous equation 24n+9m=8 and 3n-2m=6​

Answer 1

n = 14 / 15
m = -8 / 5

Explanation:

24n + 9m = 8 ------- (1) x 2

3n - 2m = 6 -----------(2) x 9

48n + 18m = 16 ------- (3)
27n - 18m = 54 --------(4)

Adding two eqn , we get ;
______________

75n = 70
n = 14 / 15

Putting value of n in eqn (2) , we get ;

14 / 5 - 2m = 6
2m = 14 / 5 - 6

2m = -16 / 5

m = -8 / 5

Answer 2

We can solve the simultaneous equation 24n + 9m = 8 and 3n - 2m = 6 by using the elimination method.

First, we need to multiply the second equation by 3 to eliminate n:

24n + 9m = 8

(3n - 2m) × 3 = 6 × 3

9n - 6m = 18

Now we have two equations with the same n coefficient, so we can subtract the second equation from the first to eliminate n:

24n + 9m = 8

-(9n - 6m = 18)

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15n + 15m = -10

We can simplify this equation by dividing both sides by 5:

3n + 3m = -2

Now we have two equations with the same m coefficient, so we can subtract the second equation from the first to eliminate m:

24n + 9m = 8

-(3n + 3m = -2)

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21n + 6m = 10

We can simplify this equation by dividing both sides by 3:

7n + 2m = 10/3

Now we have two equations with only one variable, so we can solve for one variable and substitute the value into one of the original equations to solve for the other variable:

7n + 2m = 10/3

2m = 10/3 - 7n

m = (10/3 - 7n)/2

Substitute this expression for m into the first equation:

24n + 9m = 8

24n + 9[(10/3 - 7n)/2] = 8

24n + (30/2 - 63n/2)/2 = 8

24n + 15 - 63n/4 = 8

24n - 63n/4 = 8 - 15

(96n - 63n)/4 = -7

33n/4 = -7

n = -28/33

Substitute this value of n into the second equation:

3n - 2m = 6

3(-28/33) - 2m = 6

-28/11 + 2m/11 = 2

2m/11 = 2 + 28/11

2m/11 = 50/11