In Exercises 1–5, solve by the method of your choice. Identify sy...

Question

In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

Accepted Answer

Hello. Today we're gonna be solving a system of equations. So the given system has the equations, Y is equal to three X plus two and negative seven X plus Y is equal to negative six. We can solve the system of equations using any preferred method. And if it has no solution or infinitely many solutions we need to express the answer and set notation. Okay, so how do we go about solving the system of equations? Well we can use the substitution method here. We are told that y is equal to three X plus two. We can go ahead and use this as a substitution for our second equation. So substituting y into our second equation is going to give us negative seven, X plus three, X plus two equal to negative six. Now all we have to do is just go ahead and simplify and solve for X. So negative seven, X plus three is going to give us negative four, X plus two is equal to negative six. Now what we're gonna do is subtract two from both sides of this equation and that's going to give us -4. X is equal to negative eight. Now, in order to solve for X, all we have to do is divide both sides by -4 and we get X is equal to two. So we've solved the first value for the system of equations. Now what we need to do is go ahead and take our X. Is equal to two value and plug in to any one of our original equations and solve for Y. While the easier one to work with is going to be the first equation. So if we take X and plug it into our first equation, what we get is why is equal to three times two because X is equal to two plus two, three times two is going to give us six and six plus two is going to give us eight and that's gonna be our second solution. So the solutions to the system of equation is X is equal to two and Y is equal to eight. And that means that the answer to this problem is going to be B. So I hope this video helps you in understanding how to use the substitution method and I'll go ahead and see you all in the next video.

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In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.