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Question 3(Multiple Choice Worth 1 points)

(05.02)

Choose the equivalent system of linear equations that will produce the same solution as the one given below.

4x − y = −11
2x + 3y = 5

A. −4x − 9y = −21
−10y = −30

B. 4x + 3y = 5
2y = −6

C. 7x − 3y = −11
9x = −6

D. 12x − 3y = −33
14x = −28

Respuesta :

proverbialtoast
Hello,

We want to solve the first set of equations, so we can compare it to the rest of the solutions to see which one matches.

The first equations are:
4x - y = -11
2x + 3y = 5

To solve this system of equations, multiply the second equation by -2, and then add the first equation to the new second equation. (In the second equation, when multiplied by -2, 2x becomes -4x. Add this with 4x, and it becomes 0, so you can solve for y)

We are adding:
4x - y = -11
-4x - 6y = -10

When added, we get -7y = -21 
Divide by -7 on both sides, and you get y = 3.

If we plug it into the original equation, you get 4(x)-3=-11
Add 3 to both sides, and you get 4x=-8
Divide by 4 on both sides to get x = -2.

We are now looking for an answer choice with a solution of x = -2, and y = 3.

If you look at option D, and plug in the values of x and y, you get:
12x - 3y = 12(-2) - 3(3) = -33 Checks out.
14x = 14(-2) = -28 (Checks out)

The answer is option D.
Hope this helps!


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