Question

5m-3n=16;m-6n=-7

Solve the following Equation​

Answer 1

Answer:

The two variables are $\frac{53}{7} and \frac{17}{7}$

Step-by-step explanation:

We have been mentioned here that two equations are to be solved. They are as follows:

5m-3n = 16 and m-6n = -7

Therefore we will multiply 1 with the first equation and 5 with the other one so as to make one of the variables in both equations equal:

1(5m-3n) = 1(16)

⇒ 5m - 3n = 16

5(m-6n) = (5) (-7)

⇒ 5m - 30n = -35

Now we subtract both these equations and get:

5m - 3n - (5m - 30n)  = 16 - (-35)

⇒ 5m -3n -5m + 30n = 16 + 35

⇒ 27n = 51

⇒ n = 51 ÷ 27

⇒ n = $\frac{17}{7}$

And therefore putting n we get m to be,

m - 6×$\frac{17}{7}$ = -7

⇒ m = -7 + $\frac{102}{7}$

⇒ m = $\frac{53}{7}$

Therefore the two variables are $\frac{53}{7} and \frac{17}{7}$