Solve the following system of equations. With multiplication 4x– 3y = -11 - 7x-8y= 6

Mathematics

1 answer:

Aliun [14]4 years ago

5 0

4x - 3y = -11

-7x - 8y = 6

We need to cancel out one of the variables so let's multiply the first equation by 8 and the second by 3 and aim to cancel y.

32x - 24y = -88

-21x - 24y = 18

Now we subtract,

53x = -106

x = -2

3y = 4x + 11 = 4(-2) + 11 = 3

y = 1

Answer: (x,y)=(-2,1)

Check:

4(-2) -3(1) = -8 - 3 = -11, good

-7(-2) - 8(1) = 14 - 8 = 6, good

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Neko [114]

We halve the diameter of 6 to get a radius of 3, and are given a height of 10. As we have two hemispheres, we can combine them into one sphere, so we would take the volume of a sphere with r=3 and add it to the volume of a cylinder with r=3 and h=10. Volume of a sphere is (4/3)pi*r^3 and volume of a cylinder is pi*r^2*h. Plugging in our values and adding, we get $V= \frac{4}{3} 3^3 \pi +3^2*10 \pi =36 \pi +90 \pi =126 \pi$ . This makes your answer 126*pi inches, which is roughly 395.841 inches.