​ The solution of the simultaneous equation x/2 + y/2 and x + y = 10 is given by ​

Question

The solution of the simultaneous equation \(\frac{X}{2}+\frac{y}{3}\)and x + y = 10 is given by 

(a) (6, 4) 

(b) (4, 6) 

(c) (–6, 4) 

(d) (6, –4)

Answer 1

(b) (4, 6)

\(\frac{X}{2}\) + \(\frac{y}{3}\) = 4

\(\Rightarrow\) 6 x \(\frac{X}{2}\) + 6 x \(\frac{y}{3}\) =  6 x 4

\(\Rightarrow\) 3x + 2y = 24 ..........(i)

Given, x + y = 10  \(\Rightarrow\) y = 10 – x .....(ii)

Substituting the value of y in (i), we get

3x + 2 (10 – x) = 24

\(\Rightarrow\)3x + 20 – 2x = 24

\(\Rightarrow\) x = 24 – 20 = 4

\(\therefore\) From eqn (ii), y = 10 – 4 = 6.