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Which statements are true about the ordered pair (−1,−4) and the system of equations?

x−y=3, 7x−y=−3

Select each correct answer.

 

a) The ordered pair ​ (−1,−4) ​ is not a solution to the system of linear equations.

b) The ordered pair ​ (−1,−4) ​ is a solution to the system of linear equations.

c) When ​ (−1,−4) ​ is substituted into the first equation, the equation is true.

d) When ​ (−1,−4) ​ is substituted into the second equation, the equation is false.

e) When ​ (−1,−4) ​ is substituted into the second equation, the equation is true.

f) When ​ (−1,−4) ​ is substituted into the first equation, the equation is false.

 

 

I think the answers are A, D, and F

 
hoiuu  Nov 8, 2018
edited by hoiuu  Nov 8, 2018
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Okay, again, let's try to solve here for the solution of the system.

 

Here, we can use elimination, or if you want to try; substituion. 

 

We have x-y=3 and 7x-y=-3. If we add subtract both equations, the y's will cancel out, so that's good!

 

Therefore, we get x-7x=3-(-3), which is -6x=6 and x=-1. 

 

Plugging the value of x for the value of y, we attain -1-y=3, -y=4, y=-4. So, it is a solution to the system! (B) works.

 We can try plugging in this system to see if this works for both equations. Doing so, we get -1-(-4)=3, -1+4=3, True!, (C)

 

And, for the second equation, 7(-1)-(-4)=-3, -7+3=-3, Yes! So, (E) works!

 

Thus, the answer is (B), (C), and, (E).

 
tertre  Nov 8, 2018

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