Question

How do you solve the following linear system: `3x - 6y = 9 , y = 1/2x - 3/2`?

Answer 1

Solve by substitution:

`3x - 6y = 9 , y = 1/2x - 3/2`

In the second equation the value of `y` can be substituted to the first equation:

`rarr3x-6(1/2x-3/2)=9`

Use distributive property (`a(b+c)=ab+ac`):

`rarr3x-(3x-9)=9`

`rarr3x-3x+9=9`

`rarr9=9`

So,if you see a equation ending like this,they mean that the value is possible for all real numbers.The value of `x` is all the real numbers in mathematics.

Now we know that `x` corresponds to all real numbers.So, `y` is as same as the second equation:

`=>y=1/2x-3/2`