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 going to be solving a system of equations. Using any preferred method. We are told that if the system of equations has no solution or infinitely many solutions, then we need to express the solution and set notation. So the equation is given to us is X plus seven Y. Is equal to nine. And the second equation is two X -3 Y. is equal to 18. So I'm gonna go ahead and use the method where we just go ahead and add the equations together in order to sulfur both variables. Well we want to go ahead and cancel out one of the variables from one of the equations. If I go ahead and multiply the first equation by negative two, that's gonna allow me to do so multiplying the first equation by negative two is going to give me negative two, X minus 14 Y. Is equal to negative 18. And just rewriting our second equation, we have two, X minus three. Y. Is equal to 18. And we're going to add those equations together. Negative two X plus two X. Is just going to cancel each other out negative 14 Y minus three Y. Is going to give me negative 17 Y. And negative 18 plus 18 equals to zero. So in order to Sulfur, why we just need to go ahead and divide both sides by -17. Doing so is going to give me why is equal to zero and that's going to be one of our solutions. So we have a solution for Y. But we need a solution for X. In order to get a solution for X. We can take our Y value and plug it into any one of our original equations And the easiest 1 to work with here is going to be the first equation. So if I plug in Y to our first equation, what we get is X plus seven times zero, because Y is equal to zero equal to nine, while seven times zero is just zero, which means that X is going equal to nine, which will be our second solution. So the solution to this equation is going to be X is equal to nine and Y is equal to zero, which means that the answer to this problem is going to be B. So I hope this video helps you into understanding how to solve a system of equations and I'll go ahead and see you all in the next video.

Struggling with College Algebra?

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.

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