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

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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