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Question

I can't seem to figure any of these problems out can someone help?

I'm sloving a system of equations in two variables by the addition method

1.Find the choice below which gives a first step in solving the given system of equations by the addition method.
2x - 3y = 7

2. If the system of equations given below is solved using the substitution method, what is the equation that results from solving the first equation for x, and substituting into the second equation?
x - 7y = 10

2x + 4y = 15

Now I can't figure out how to do this

It's Square Roots.

3.What is √ 196y^10 ? Assume y represents a positive value.

4 Simplify√ 8x^3 as much as possible. Assume x represents a positive value.

5.What is the simplified sum of √3+√12

thanks

Answer 1

1) There is only one equation given. Don't you need a second one to have a system?

Which step to take next depends on how the two equations relate to each other (in particular what the coefficients of x and y are in both)... so it's hard to answer without seeing both. For example, if your two equations are:

7x + 3y = 10
9x - 6y = 3

... then the first step would be to multiply the top equation by two (14x + 6y = 20). Then adding the two equations cancels out the y term (+6y in one and -6y in the other), and you get 23x = 23.

2)
(a) Solve the first equation for x:

x - 7y = 10
x = 10 + 7y

(b) Substitute into the second equation, replacing "x" with "10+7y" (which we've shown above is the same thing):

2x + 4y = 15
2(10+7y) + 4y = 15
20 + 14y + 4y = 15
18y = -5
y = -5/18

I solved all the way, but the "equation which results from solving and substituting" (the actual question) is: 2(10+7y) + 4y = 15

3) √(196y^10)

I assume you mean the square root of the entire quantity. You need to know these things to solve this:
(a) √(ab) = √(a) * √(b) (you can separate things out)
(b) √(x^y) = x^(y/2) (square root divides exponent by two)
(c) 196 is a perfect square (14^2)

√(196*y^10) =
√(196) * √(y^10) =
14 y^5

4) Same rules as previous:

√(8x^3) =
√(4*2*x^2*x) =
√4 * √(x^2) * √(2x) =
2x * √(2x)

That's as far as it can be simplified.

5) More of the same

√3 + √12 =
√3 + √(4*3) =
√3 + √4*√3 =
√3 + 2√3 =
3√3

Answer 2

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Answer 3

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