Question

Q6- If x= m and y= n is the solution of the equations
x + y = 7 and 2x - y = 5, then the values of m and n are
respectively
(a) 3 and 4
(b) 4 and 3
(c) 2 and 9
(d) 8 and -1
(e) None of these​

Answer 1

✬ The value of m is 4 and n is 3.Option(b)4 and 3.✬

Step-by-step explanation:

Given:-

• If x = m and y = n is the solution of the equations x + y = 7 and 2x - y = 5.

To find:-

• Value of m and n

Solution:-

• Equation 1 - m + n = 7
• Equation 2 - 2m - y = 5
• Substituting the equation 1 with equation 2

$\\ :\implies\sf{m + \cancel{n }= 7} \\ \\ :\implies\sf{2m - \cancel{n} = 5} \\ \\ - - - - - - - - - - - \\ \\ :\implies\sf{3m = 12} \\ \\ :\implies\sf{m = \frac{\cancel{12}}{\cancel{3}}} \\ \\ :\implies \underline{\boxed{\frak{m = 4}}} \: \red{ \bigstar} \\ - - - - - - - - - - -$

• Now,Putting the value of m in the place of equation 2 to find the value of n.

$\\ :\implies\sf{2(4) - n = 5} \\ \\ :\implies\sf{8 - n = 5} \\ \\ :\implies\sf{ - n = 5 - 8} \\ \\ :\implies\sf{ \cancel{- } \: n = \cancel{- } \: 3} \\ \\ :\implies \underline{\boxed{\frak{n = 3}}} \: \blue{ \bigstar}$

Therefore,

• ∴ Hence,The value of m and n is 4 and 3.