This is the basic and exam oriented question from linear equations in two variables in which we have given two equations x/3+y/2=3, x-2y=2 and we have been asked to find the value of variables x and y from the given equations in such a way that it has a unique solution
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 3D, question no 3
These equations are of the forms: a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
where, a1 = 2, b1= 3, c1 = -18 and a2 = 1, b2 = -2, c2 = -2
For a unique solution, we must have: a1/a2 ≠ b1/b2 , i.e., 2/1 ≠ 3/−2 Hence, the given system of equations has a unique solution. Again, the given equations are:
2x + 3y – 18 = 0 …..(iii)
x – 2y – 2 = 0 …..(iv)
On multiplying (i) by 2 and (ii) by 3, we get:
4x + 6y – 36 = 0 …….(v)
3x – 6y – 6 = 0 ……(vi)
On adding (v) from (vi), we get:
7x = 42 ⇒x = 6
On substituting x = 6 in (iii),
we get: 2(6) + 3y = 18
⇒3y = (18 – 12) = 6
⇒y = 2
Hence, x = 6 and y = 2 is the required solution