1. ## Help with elimination-substitution

The Jones's and the Johnsons want to see who sleeps more, women or men. The Jones family has 1 female and 3 males. On the night of the test the Jones family slept a total of 43 hours. The Johnson family has 3 males and 4 females and their total sleep was 60.72 hours.
How many hours does each male and female sleep, assuming that all males sleep the same amount of hours and all females sleep the same amount of hours.

Ok, cool.
So...
3x+y=43
3x+4y=60.72
Then...
5y=103.72
then...
y=20.74

Then when I substitute it it comes out wrong. Have I already made a mistake?

Could someone please just help me through this?

2. ## Re: Help with elimination-substitution

Originally Posted by Russellmuscle387
The Jones's and the Johnsons want to see who sleeps more, women or men. The Jones family has 1 female and 3 males. On the night of the test the Jones family slept a total of 43 hours. The Johnson family has 3 males and 4 females and their total sleep was 60.72 hours.
How many hours does each male and female sleep, assuming that all males sleep the same amount of hours and all females sleep the same amount of hours.

Ok, cool.
So...
3x+y=43
3x+4y=60.72
Then...
5y=103.72
then...
y=20.74

Then when I substitute it it comes out wrong. Have I already made a mistake?

Could someone please just help me through this?
First you need to ask yourself if that answer makes sense. Do you know many people that sleep 20.74 hours per day?

2nd you need to be careful.

You system of equations is correct

$\displaystyle \begin{matrix}3x & + & y &=& 43 \\ 3x & + & 4y & = & 60.72 \end{matrix}$

Now you need to multiply the top equation by -1 and add it to the bottom equation (or vice versa). This gives

$\displaystyle \begin{matrix}-3x & - & y &=& -43 \\ 3x & + & 4y & = & 60.72 \\ \hline & & 3y & = & 17.72 \end{matrix}$