To solve the following linear system by elimination, Brent first multiplied each equation by 10. Explain why he did this step. Complete the solution.
0.3x - 0.5y = 1.2
0.7x - 0.2y = -0.1

Question

To solve the following linear system by elimination, Brent first multiplied each equation by 10. Explain why he did this step. Complete the solution. 
0.3x - 0.5y = 1.2
0.7x - 0.2y = -0.1

misty1212 · Answer

HI!!

shelby1290 · Answer

Hey

misty1212 · Answer

multiply by 10
get rid of annoying decimals

misty1212 · Answer

$$0.3x - 0.5y = 1.2\
0.7x - 0.2y = -0.1$$
$$3x - 5y = 12\
7x - 2y = -1$$

shelby1290 · Answer

so are you saying that he multiplied 10 by 0.3....multiplied 10 by 0.5 and multiplied 10 by 1.2?

misty1212 · Answer

yeah if u multiply one part by 10, u gotta multiply all by 10

shelby1290 · Answer

Okay so the answer is: 
Brent multiplied by 10 to get rid of the decimal numbers

misty1212 · Answer

yes

doc.brown · Answer

$$1+1+1=3$$$$10+10+10=3\times 10$$

doc.brown · Answer

The numbers are still there, I think Brent multiplied by 10 to get rid of the decimal places.

shelby1290 · Answer

Okay should i add in what misty said before about how ...
you'd get 3x -5y = 12

shelby1290 · Answer

@doc.brown ^

misty1212 · Answer

no

misty1212 · Answer

$$3x - 5y = 12\
7x - 2y = -1$$ u still have 2 do more work

shelby1290 · Answer

okay so is there anything that i should calculate at all?

misty1212 · Answer

multiply the first by 2, the second by -5 and add
the y terms will go bye bye

doc.brown · Answer

Only if you want to follow the instructions, which say complete the solution.

shelby1290 · Answer

@misty1212 and after doing that I'll find the solution, right?

shelby1290 · Answer

If i multiply the first equation by 2 and the second by -5 and add the y terms

shelby1290 · Answer

I'm still a little confused on what I'm supposed to write down

doc.brown · Answer

You want to know what x is.  One way, is to divide the first one by 3.

shelby1290 · Answer

0.3 divided by 3= 0.1 
0.5 divided by 3= 0.16
1.2 divided by 3=0.4

doc.brown · Answer

Ah, sorry, I thought you were starting from$$3x - 5y = 12\
7x - 2y = -1$$

shelby1290 · Answer

oops

shelby1290 · Answer

3 divided by 3= 1 
5 divided by 3=1.6
12 divided by 3=4

doc.brown · Answer

I'd do this, it's less work.$$3x - 5y = 12\\frac{3x}{3} - \frac{5y}{3} = \frac{12}{3}\\frac{\cancel{3}x}{\cancel{3}} - \frac{5y}{3} = \frac{12}{3}\x-\frac{5}{3}y=4\x=4+\frac{5}{3}y$$

shelby1290 · Answer

thank you 
what's x and y

doc.brown · Answer

I don't know, stick x into the second equation.

shelby1290 · Answer

did you find it already?

shelby1290 · Answer

or is that what i'm supposed to do
but btw i'm not exactly sure how to solve everything from here. Fractions confuse me.

doc.brown · Answer

No they don't, your teacher confused you.

@misty1212 was having you make the y's equal and subtract them to get x by itself.

I was getting x alone on one side and substituting it in to the other equation to get y by itself.

Do you have a preference?

shelby1290 · Answer

Nah but I'll just follow what you're doing and get x by itself

shelby1290 · Answer

I'll do whatever it takes to get the correct answer!

shelby1290 · Answer

so was misty's answer wrong?

doc.brown · Answer

They all work, from the first equation I got$$\color{red}{x=4+\frac{5}{3}y}$$Stick that in here$$7\color{red}{x}-2y=-1$$

shelby1290 · Answer

7(4 + 5/3y) -2y = -1

doc.brown · Answer

Distribute the 7.
7(4)+7(5y/3)...

shelby1290 · Answer

28+ 35y/3

doc.brown · Answer

$$28+\frac{35}{3}y-2y=-1$$Now what?

shelby1290 · Answer

do i bring 28 to the other side?

shelby1290 · Answer

then it would become -1-28

doc.brown · Answer

yup, then add the ys

shelby1290 · Answer

okay so 37/3 ?

shelby1290 · Answer

hold on, shouldn't i be subtracting not adding?

shelby1290 · Answer

then the answer is: 33/3y=-29

shelby1290 · Answer

@doc.brown ^

doc.brown · Answer

Can you imagine a half?

shelby1290 · Answer

why, what do you mean?

doc.brown · Answer

What happens if you add a quarter to a half, what do you get?

shelby1290 · Answer

3/4

doc.brown · Answer

That's right, the bottom number has to be the same and you add up the tops.

doc.brown · Answer

$$\frac{35}{3}y-\frac{6}{3}y$$

shelby1290 · Answer

@doc.brown 29/3

doc.brown · Answer

$$\frac{29}{3}y=-29$$

shelby1290 · Answer

yes

shelby1290 · Answer

@doc.brown what's the next step

shelby1290 · Answer

divide both sides but by what

doc.brown · Answer

You want the y to be alone, multiply each side by 3/29

shelby1290 · Answer

1y=-3

doc.brown · Answer

Good, so if we know $y=-3$
What's$$x=4+\frac{5}{3}y$$

shelby1290 · Answer

x=4+5/3(-3) =-1 
so the answer is -1 
@doc.brown

doc.brown · Answer

Does it work, does $x=-1$ and $y=-3$ if$$0.3x - 0.5y = 1.2$$

shelby1290 · Answer

0.3(-1) - 0.5 (-3) =1.2 
Yea it works

shelby1290 · Answer

@doc.brown Thank you so much for all the help!