If the system of linear equations 2x+3y= 7 and 2ax + (a + b) y = 28

Q) If the system of linear equations 2x+3y= 7 and 2ax + (a + b) y = 28 have infinite number of solutions, then find the values of ‘a’ and ‘b’.

Ans:

We know linear equations can be written as ax + by + c=0

Therefore, in given equations, 2x+3y=7 ——(1)

And, 2ax+ (a + b) y = 28 ——-(2)

In equation (1), let a₁=2; b₁=3; c₁=7

And in (2), let a₂= 2a ; b₂ = (a + b) ; c₂ = 28

We know, when system of linear equations have infinite solutions, then

$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$

Therefore,

$\frac{2}{2a} = \frac{3}{a + b} = \frac{7}{28}$

Solving equations separately, we get:

a = 4 and b = 8

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