Question

Find the value of a and b for which the following system of linear equations has infinitely many solutions:
(i) 2x+3y= 7 and 2ax+ ay=28- by.
(ii) 2x+3y=7 ,(a-b)x +(a+b)y =3a +b-2
(iii) 2x-(2a+5)y =5, (2b+1)x -9y =15​

Answer 1

Answer:

We can write this out as an algebraic formula. Let X = the weight of the brick.

X = 1 + 1/2 * X

What we want is to have X alone on one side of the equation with no other X’s on the other side. To do this, let’s first multiply both sides of the equation by 2. We can add to, subtract from, multiply, or divide equations all we want as long as we do the same operation to both sides.

2 * (X) = 2 *(1 + 1/2 * X)

2 * X = 2 + X

Now let’s subtract X from both sides.

2 * X - X = 2

X = 2

..

Answer 2

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Hence the value of A is 4 and b is 8.

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