In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 3) x + 3y = 11 x - 5y = - 13

Question

Ordered pair (2, 3) with two linear equations for a systems of equations exercise.

Accepted Answer

Hello. Today we're going to be determining whether the ordered pair given satisfies the system of equations shown below. So the ordered pair given to us is negative two comma six. And since the ordered pairs of the form X comma Y. This means that X is equal to negative two and Y is equal to six. Now in order to determine whether this satisfies the system of equations. What we're going to need to do is substitute in X and Y into both of the equations. And if it makes both of the equations true then it satisfies the system of equations. So let's go ahead and start by plugging in X and Y into equation one equation, one is two, X plus Y is equal to two, plugging in X and y is going to give us two times negative two plus y, which is six and that should equal to two while two times negative two is going to give us negative four and negative four plus six is going to give us positive two and that is equal to two. So the first equation is true. Now we want to go ahead and check the second equation. The second equation is five, X minus y is equal to negative 16, plug in X and y is going to give us five times negative two minus y which is minus six is equal to negative 16. 5 times negative two is going to give us negative 10 and negative minus six is going to give us negative 16 which is equal to negative 16. So the point satisfies the second equation. And since the point satisfies both the 1st and 2nd equation, that means that it satisfies the system of equations, so the answer to this problem is going to be a So I hope this video helps you in understanding how to approach this type of problem, and I'll go ahead and see you all in the next video.

In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 3) x + 3y = 11 x - 5y = - 13

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