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In Exercises 7 - 10, determine whether each ordered pair is a solution of the system of equations

$ \left\{\begin{array}{l}4x^2 + y = 3\\-x - y = 11\end{array}\right. $

(a) $ (2 , -13) $

(b) $ (2 , -9) $

(c) $ (- \dfrac{3}{2} , - \dfrac{31}{3}) $

(d) $ (- \dfrac{7}{4} , - \dfrac{37}{4}) $

$a(2,-13)$

$b(2,-9)$ is not a solution to this system of equations.

$c\left(-\frac{3}{2},-\frac{31}{3}\right)$ is not a solution to this system of equations.

$d \left(-\frac{7}{4},-\frac{37}{4}\right)$ is a solution to this system of equations.

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Missouri State University

Campbell University

Oregon State University

Numerade Educator

Okay, so we're asked to see if the's or repairs air solutions for this system of equations. And we can do this just by solving for X and Y and seeing if any of those options are here. So you can do this by so we have four x squared plus y is equal to three. If we subtract, uh, we just add this equation to eradication. Throughout it, you get a four x squared minus X. The wise cancel equals 14. So this is just a quadratic that we could assault x four, get four X squared minus X minus 14 is equal to zero. Yet for X factor this X and then a seven. And to look at here, get negative eight X plus seven X will give us the negative X that we need than a seven times united to give us the negative 14 that we need. So this is it. This works, um, then can sell for X, and we get the X equal to negative seven forks. That X is also equal to positive, too. So we have a couple of candidates here from here. He could tell that this is this is not an answer. But then we can look at this and see maybe if one of these are the answer so we can put these values into our equation. I'm just gonna use the bottom one here just cause it seems a little easier to work with S O negative X negative. Negative summon forth, since positive 7/4 minus y is equal to 44 over four. I'm just rewritten. 11 in this four. Make it easier to combine these numbers so we get that Y is equal to negative 37 quartz. And so there we have one of our answers is D. So now let's see about two, um, negative to minus y is equal to 11. Get negative wise equal to 13. So why is equal to negative 13? And so this is also a solution. Um, and the solutions are just where these two graphs intersect each other. So if you want to grab it, they would intersect each other at these points. So those were the