Question

find the value of a so that the lines (a+b)x + (a-b)y =4 and x+y = 1 are the same lines

Answer 1

@cgoel, So we know x + y = 1 is a given line right?

Answer 2

yes

Answer 3

And we want (a + b)x + (a - b)y = 4 to be the same line right?

Answer 4

correct

Answer 5

So what we can do is multiply both sides of x + y = 1 by four. And if we do that we get

4x + 4y = 4. Do you agree?

Answer 6

yes i agree, that makes sense

Answer 7

So if both lines are the same, and both lines equal the same value, then the coefficients of each term must also be the same as well right?

Answer 8

In other words

a + b = 4
a - b = 4

Do you agree?

Answer 9

sure, definatley

Answer 10

Okay, and we only need to solve for variable a at this point. Do you see a way to do that?

Answer 11

um, no...

Answer 12

If we added both equations together, we could eliminate variable b and solve for a.
It works like this. We simply add the corresponding like terms of each equation together like so:
(a + a) + (b - b) = 4 + 4

Answer 13

So we end up with

2a = 8

Answer 14

Do you see that?

Answer 15

oh yeah, now i see, so a =4. great! i also have another question

Answer 16

Just out of curiosity, do you know what b equals?