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3 years ago

2. Use the linear combination method to solve the system of equations. Explain each step of your solution

Mathematics

1 answer:

sladkih [1.3K]3 years ago

3 0

x = - 3

y = -2

Step-by-step explanation:

3x - 8y = 7

x +2y = -7

We standardize the coefficient of one variable such that it addition will result to zero;

3x - 8y = 7

(x +2y = -7)4

Then multiply the one equation with a constant (this case 4) to get;

3x – 8y = 7

4x + 8y = - 28

We add the two equations;

3x – 8y = 7

4x + 8y = - 28

7x = - 21

x = -21 / 7

x = - 3

Now we evaluate y by replacing the value of x with -4 in one of the equation;

x +2y = -7

-3 +2y = -7

2y = -7 + 3

2y = - 4

y = -2

Learn More:

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Step-by-step explanation:

Remember that in all these cases, we have a specified method to use, the washer method, disk method, and the cylindrical shell method. Keep in mind that the washer and disk method are one in the same, but I feel that the disk method is better as it avoids splitting the integral into two, and rewriting the curves. Here we will go with the disk method.

$\mathrm{V\:=\:\pi \int _a^b\left(r\right)^2dy\:},\\\mathrm{V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy}$

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$V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=\pi \cdot \int _1^3\left(1+\frac{2}{y}\right)^2-1dy\\\\\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\= \pi \left(\int _1^3\left(1+\frac{2}{y}\right)^2dy-\int _1^31dy\right)\\\\$

$\int _1^3\left(1+\frac{2}{y}\right)^2dy=4\ln \left(3\right)+\frac{14}{3}, \int _1^31dy=2\\\\=> \pi \left(4\ln \left(3\right)+\frac{14}{3}-2\right)\\=> \pi \left(4\ln \left(3\right)+\frac{8}{3}\right)$

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