Sole the following system of equations 8x-3y=13 -3x-8y=-14

Mathematics

1 answer:

user100 [1]3 years ago

8 0

The system reads:

8x-3y=13

-3x-8y=-14

Solve this by solving for one variable at a time by cancelling the other. We will begin by solving for y and cancelling x. To do this, you need to find the least common multiple (LCM) of the x variables and multiply both equations by the number which will make them equal the LCM. For 8 and 3, the LCM is 24, so you will multiply the top equation by 3 and the bottom one by 8.

*****In order for the variables to cancel, the signs need to be opposite. In this system, one is already positive and the other negative; if this were not the case, one of the equations would have needed to be multiplied by a negative number.*****

The system becomes:

24x-9y=39

-24x-24y=42

Now, you can combine the equations by adding them:

-33y=81

Solve for y:

*Divide both sides by -33*

y=27/11

To find x, you can select one of the given equations, plug in 27/11 for y, and solve for x. We'll use the first equation:

8x-3(27/11)=13

8x-81/11=13

*Add 81/11 to both sides*

8x=224/11

*Divide both sides by 8*

x=28/11

Hope this helps!!

You might be interested in

Which correctly uses bar notation to represent the repeating decimal for 6/11?

Alexandra [31]

Answer:

Step-by-step explanation:

i took the quiz

8 0

3 years ago

Simplify this expression: i ^257

Katarina [22]

Okay!
What is i?
i = √(-1)

What is i^2?
i^2 = √(-1) * √(-1)

Note: Whenever you multiply two square roots with the same numbers you get this:

√(a^2)

Or in this case:

√(-1 * -1) = -√(1) = -1

So,
i^2 = -1

What does i^3 equal?
i^3 = √(-1) * √(-1) * √(-1) = 1 * √(-1) = √(-1) which is... -i

What does i^4 equal?
i^4 = √(-1) * √(-1) * √(-1) * √(-1) = √(-1 * -1 * -1 * -1) = 1

After that the cycle does it thing and cycles back.
So, with this information we can figure out what i^157 equals.

Knowing long division here helps a lot!
Take 157 and divide it by 4 using long division. If you don't know it, I'll show you how to do it to the best of my abilities. (Refer to the picture. If you have any questions about it then ask. Even if the question is... what does this say?)

After using long division we see that we get:
39 with a remainder of 1.

What that means is:
(i^4)^39 is what we have. The remainder of 1 means that we have 1 i left. So our answer is i.

The reason we divided by 4 and not some other term is because i^4 = 1, so it is easy to work with. In this case (i^4)^39 still just equals 1. Which leaves our remainder as our answer.

So once again the final answer is:
i

As for i^257. I'll show you the answer, but I won't give the work for this one. I'd recommend you try it out for yourself.

i^257 = (i^4)^64 * i = i.

I hope that I helped, and if you have any further questions then ask away!