# Solve? 0.45x+0.65y=15.35 9x+13y=305

Apr 4, 2018

No solution

#### Explanation:

$0.45 x + 0.65 y = 15.35$ and $9 x + 13 y = 305$

First lets make the first equation simpler by multiplying throughout by 100

$45 x + 65 y = 1535$

Now divide both sides by 5

$9 x + 13 y = 307$

Now the two equations are $9 x + 13 y = 307$ and $9 x + 13 y = 305$

Now, these are parallel lines hence they do not intersect hence they have no common point and thus no common solution

So the two equations have no solution

(Another way to look at it: No matter what you put as x and y how can 9x+13y be equal to 305 and 307 at the same time? No solution)

Apr 4, 2018

$0.45 x + 0.65 y = 15.35$

Multiply throughout the equation by $20$, just to make it look simpler.

[I got to $20$, as I first decided to multiply by $100$ to get whole numbers, n then divide by $5$ as each term is divisible by $5$. So I multiply by a net $\frac{100}{5}$ (i. e. $20$). You could also make two steps out of it if that's convenient to you.]

$\implies 9 x + 13 y = 307$

And the given second equation is $9 x + 13 y = 305$

Note that the $x$ and $y$ coefficeints are same, hence the lines are parallel (and do not intersect). So, these do not have a solution.