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

##### 2 Answers

#### Explanation:

There are numerous ways But i shall do the easiest one

Now the Final part;

Plug the value in ---1

Now there is the graphical and mechanical way of solving this

Mechanical(Boring ,No fun);

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

#### Explanation:

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

In the other equation, we have

#3x + 7y = 47#

We know that we can write

#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

#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;