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Mathematics
OpenStudy (anonymous):

Did I do this problem right? Solve the linear system: 4x+3y=1 and -3x - 6y = 3 7x - 9y = -2

OpenStudy (anonymous):

Nope.

OpenStudy (anonymous):

You need to find an \(x\) and \(y\) value.

OpenStudy (anonymous):

First eliminate the \(y\) values.

OpenStudy (anonymous):

Since you have \(3y\) and \(-6y\). As things stand \(3y-6y=-3y\). However if you multiply the first one by \(2\) then \((2)3y-6y=6y-6y=0\).

OpenStudy (anonymous):

So we multiply the first equation by \(2\).\[ 4x+3y=1 \to 8x+6y=2 \]

OpenStudy (anonymous):

Now you can add the equations: \[ \begin{split} &8x&+& 6y &=& 2 \\ +&-3x& -& 6y &=& 3\\ &5x&&&=&5 \end{split} \]This means \(x=1\)

OpenStudy (solomonzelman):

x = 1 and y = -1

OpenStudy (anonymous):

okay so how do you get y?!

OpenStudy (solomonzelman):

plug in 1 for x and solve for y

OpenStudy (anonymous):

To get \(y\) you plug \(1\) into \(x\) for either equation: \[ -3x - 6y = 3\\ -3(1) - 6y = 3 \]

OpenStudy (solomonzelman):

C?

OpenStudy (anonymous):

yes, so just to make sure im writing it correctly, its (1,-1) ?

OpenStudy (solomonzelman):

yes

OpenStudy (solomonzelman):

U r correct!

OpenStudy (anonymous):

thank you very much to the both of you!

OpenStudy (solomonzelman):

A/t else I can help u w/?

OpenStudy (anonymous):

um, let me see

OpenStudy (solomonzelman):

I am ready

OpenStudy (anonymous):

what is the slope of the line of 4x-5y=9?

OpenStudy (solomonzelman):

Lets work it together, Do u know the slope formula?

OpenStudy (anonymous):

y=mx+b ?

OpenStudy (solomonzelman):

Ok

OpenStudy (solomonzelman):

Try to put this equation in a standard format (like y=mx+b)

OpenStudy (solomonzelman):

Do u know how to do this?

OpenStudy (anonymous):

y=4x+5?

OpenStudy (solomonzelman):

the original equation was 4x-5y=9, and how did you get this, no!.... basically solve for y (in terms of x)

OpenStudy (anonymous):

but 4 doesnt go into 9, im so confused!

OpenStudy (solomonzelman):

OK! 4x-5y=9 5y=9+4x y = 9/5 + 4/5x (lets put is in a standard form the same way as y=mx+b) y= 4/5x +9/5

OpenStudy (solomonzelman):

Now answer the following for me, what is the slope and what is the y intercept?

OpenStudy (anonymous):

i honestly have no idea, i dont get this.

OpenStudy (solomonzelman):

What don't u get?

OpenStudy (solomonzelman):

A/t?

OpenStudy (solomonzelman):

lets follow the steps together. STEP 1 4x-5y=9 Do u understand y i did this?

OpenStudy (solomonzelman):

I wrote the equation out, next...

OpenStudy (solomonzelman):

5y=9+4x what am I doing in this STEP ? do u know?

OpenStudy (anonymous):

oh i do know that you have to put y first.

OpenStudy (solomonzelman):

Yes there u go! Eliminate the Y so i preformed the following steps 4x-5y=9 5y=9+4x y = 9/5 + 4/5x (lets put is in a standard form the same way as y=mx+b) y= 4/5x +9/5

OpenStudy (solomonzelman):

C ?

OpenStudy (anonymous):

kinda so how do you add the 4/5x + 9/5?

OpenStudy (solomonzelman):

I don't add 4/5x + 9/5, I can't and I don't have to! Once I have this equation- y= 4/5x +9/5 , I am done! Compare this to y=mx+b and tell me, in the equation that I got, what is the slope?

OpenStudy (anonymous):

so it would just be 4/5?

OpenStudy (solomonzelman):

Yes! CORRECT!

OpenStudy (anonymous):

THANK YOU!

OpenStudy (solomonzelman):

and the Y intercept would be what?

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