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 = −19
−10y = −30
B.)4x + 3y = 5
2y = −6
C.)7x − 3y = −11
9x = −6
D.) 12x − 3y = −33
14x = −28

Question

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 = −19
−10y = −30
B.)4x + 3y = 5
2y = −6
C.)7x − 3y = −11
9x = −6
D.) 12x − 3y = −33
14x = −28

celinegirl · Answer

D?

pooja195 · Answer

D is incorrect 
the given system of equations solution is
(-2,3) 
which of these has the same coordinate pair?

anonymous · Answer

First, let's solve the given system of equations.  :D
Let's examine the first equation in there:
$$4x-y=-11$$
Let's solve for y. First, subtract 4x from both sides:
$$-1y= -4x-11$$
Then, divide by -1 on both sides to get:
$$y=4x+11$$
Now, let's look at our new equation and the 2nd given equation:
$$2x+3y=5$$$$y=4x+11$$
By substitution, we can plug in ''y'' into the 2nd equation:
$$2x+3(4x+11)=5$$
Now, distribute the 3 to both terms inside the parentheses:
$$2x+12x+33=5$$
You can add ''2x'' and ''12x'' together, which simplifies our equation to:
$$14x+33=5$$
Now, let's solve for x. Subtract 33 from both sides:
$$14x=-28$$
Simply divide both sides 14 to get:
$$x=-2$$
Now that we know x, we can plug it into our ''y'' equation:
$$y=4(-2)+11$$
$$y=-8+11=3$$
So, y=3.
Our solutions for the given system of equations are: (-2,3).
We must find another system of equations that has those same solutions.
Let's look at our choices. Looking at D, the second equation is:
$$14x=-28$$
This means that:
$$x=-2$$
Let's plug that into the first equation in D:
$$12(-2) - 3y= -33$$
This can be simplified to:
$$-24-3y= -33$$
We can solve for y by first adding 24 to both sides:
$$-3y=-9$$
Divide both sides by -3 to get:
$$y=3$$
So, our solution for the system of equations in D is (-2,3). These are the same solutions that we got for our given system of equations. Therefore, the correct answer choice is D. If you have any more questions, please let me know.   :D

pooja195 · Answer

Then there are 2 correct answers because A works too.

celinegirl · Answer

thank you

anonymous · Answer

You are welcome! I messaged her saying that A also works.   :D
If you ever need help, please message or tag me. If I am online, I will receive it and be able to help you.  ^^