Question

Write four solutions of the equation m+ n = 15​

Answer 1

Step-by-step explanation:

10 +5

5+10

13+2

14+1

7+8

8+7

Answer 2

The 4 solutions of the equation are (1,14), (2,13), (3,12), and (4,11). [ The first value is of 'm' and the second of 'n' ].

The given equation is $m+n=15$. It has 2 variables i.e. 'm' and 'n'.

As the number of variables i.e. 2 is greater than the number of equations i.e.1, we cannot solve the system of variables.

So, we assume the value of one variable and find the corresponding value of the other variable using the equation. We perform this procedure N times to get N solutions.

Solution 1 : m = 1

Let us assume the value of one variable i.e. m = 1

So, the corresponding value of the other variable i.e. 'n' is :  

            $m + n = 15\\1 + n = 15\\n = 15-1\\n=14$

(1, 14) is one solution of the given equation.

Solution 2 : m = 2

Let us assume the value of one variable i.e. m = 2

So, the corresponding value of the other variable i.e. 'n' is :  

            $m + n = 15\\2 + n = 15\\n = 15-2\\n=13$

(2, 13) is one solution of the given equation.

Solution 3 : m = 3

Let us assume the value of one variable i.e. m = 3

So, the corresponding value of the other variable i.e. 'n' is :  

            $m + n = 15\\3 + n = 15\\n = 15-3\\n=12$

(3, 12) is one solution of the given equation.

Solution 4 : m = 4

Let us assume the value of one variable i.e. m = 4

So, the corresponding value of the other variable i.e. 'n' is :  

            $m + n = 15\\4 + n = 15\\n = 15-4\\n=11$

(4, 11) is one solution of the given equation.

Hence, the 4 solutions of the equation are (1,14), (2,13), (3,12), and (4,11).

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