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

Sep 25, 2015

$y = 8 , x = - 3$

#### Explanation:

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

There are numerous ways But i shall do the easiest one

Now the Final part;

Plug the value in ---1

$7 y = 41 - 5 \left(- 3\right)$

$7 y = 41 + 15$

$7 y = 56$

$y = 8$

Now there is the graphical and mechanical way of solving this

Mechanical(Boring ,No fun);

Sep 25, 2015

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

#### Explanation:

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

$x = \frac{41 - 7 y}{5}$

In the other equation, we have

$3 x + 7 y = 47$

We know that we can write $\frac{41 - 7 y}{5}$ instead of $x$. So we get

$3 \cdot \frac{41 - 7 y}{5} + 7 y = 47$

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

$\frac{123 - 21 y}{5} + 7 y = 47$

$123 - 21 y + 35 y = 235$

$14 y = 112 \implies y = 8$

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

$5 x + 7 y = 41$

$5 x + 56 = 41$

$5 x = - 15 \implies x = - 3$

$3 x + 7 y = 47$

$3 x + 56 = 47$

$3 x = - 9 \implies x = - 3$

So the result is; $\left(- 3 , 8\right)$