36. (ix) 2x + 3y = 7
2ax + ay = 28 - by
find the values of a and b for which the following system of equation has infinitely many solution.
Answers
Given: Two equations, 2x + 3y = 7 , 2ax + ay = 28 - by
To find: Value of a and b for which the following pair of linear equations has infinite number of solutions.
Solution:
- As we have given the two equations, we first need to write the coefficients in an order.
- So the coefficients should be written as if equation is Ax + By = C,
- So, in first equation:
2x + 3y = 7
A1 = 2, B1 = 3, C1 = 7
- in second equation:
2ax + ay + by = 28
A2 = 2a, B2 = a+b, C2 = 28
- Now for infinitely many solutions, we have the condition that:
A1/A2 = B1/B2 = C1/C2
- So applying this in the above equations, we get:
2 / 2a = 3/a+b = 7/28
- Now solving any two of the above, we get:
2/2a = 7/28
1/a = 1/4
a = 4
- Now solving next two from above, we get:
2/2a = 3/a+b
1/4 = 3/4+b
4+b = 12
b = 8
Answer:
So, for a = 4 and b = 8 , the following pair of linear equations has infinite number of solutions.
Answer:
Frist adjectives the equation in proper form.... ☺️☺️☺️hence by doing these question become to easy........
