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Does someone mind helping me with this problem? Thank you!

Does someone mind helping me with this problem? Thank you!-example-1
User Darkdog
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1 Answer

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Answer:

(x, y) = (-2, 2)

Explanation:

You want to solve by elimination the system 4x +5y =2; -2x +2y = 8.

Observation

The x-coefficients are related by the integer factor -2. The y-coefficients are not related by an integer factor. This suggests it will be easier to eliminate the x-terms.

Since the x-terms have opposite signs, we can multiply the second equation by 2 and add it to the first to eliminate the x-terms.

Solution

Adding double the second equation to the first, we have ...

(4x +5y) +2(-2x +2y) = (2) +2(8)

9y = 18 . . . . . . . . . . simplify

y = 2 . . . . . . . . . . . divide by 9

Using the second equation to find x, we have ...

-2x +2(2) = 8

-2x = 4 . . . . . . . subtract 4

x = -2 . . . . . . . . divide by -2

The solution is (x, y) = (-2, 2).

__

Additional comment

As a check on our solution, we have attached a graphical solution that gives the same result.

Does someone mind helping me with this problem? Thank you!-example-1
User Altabq
by
7.4k points

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