Question

How do you determine the solution in terms of a system of linear equations for 5x+7y=41 and 3x+7y=47?

Answer 1

`y = 8 , x = -3`

Explanation:

`5x+7y=41 ,3x+7y=47`

There are numerous ways But i shall do the easiest one

Now the Final part;

Plug the value in ---1

`7y = 41 - 5(-3)`

`7y = 41 + 15`

`7y = 56`

`y = 8`

Now there is the graphical and mechanical way of solving this

Mechanical(Boring ,No fun);

Answer 2

You should write a variable in terms of the other variable.

Explanation:

`5x + 7y = 41` so we can say that `5x = 41 - 7y`, so

`x = (41 - 7y)/5`

In the other equation, we have

`3x + 7y = 47`

We know that we can write `(41 - 7y)/5` instead of `x`. So we get

`3 * (41 - 7y)/5 + 7y = 47`

In order to solve this equation, you need to expand it;

`(123 - 21y)/5 + 7y = 47`

`123 - 21y + 35y = 235`

`14y = 112 implies y=8`

Then you can easily find `x` by writing `8` insted of `y` in one of the equations:

`5x + 7y = 41`

`5x + 56 = 41`

`5x = -15 implies x = -3`

`3x + 7y = 47`

`3x + 56 = 47`

`3x = -9 implies x = -3`

So the result is; `( -3 , 8)`