In Exercises 31–42, solve by the method of your choice. Identi...

Question

In Exercises 31–42, 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. y = 3x - 5 21x - 35 = 7y

Accepted Answer

Hey everyone welcome back in this problem. We are asked to solve the system of equations. And the system we're given is y equals 17. X minus 51 51 X is equal to minus 153. Sorry, 51 x minus 253 is equal to three Y. Okay, so let's go ahead and just label these equations case. So it's easier to refer to them. We have equation one Y equals 17, X minus 51. We have an equation to 51 X minus 153 equals three Y. All right. We can use any method we'd like here because we haven't the question hasn't specified. Let's go ahead and use the substitution method since we already have Why isolated an equation one? Okay, in the substitution method we're going to isolate one of the variables again. We've already done that with why or why is already done for us? We can substitute it into the other equation that allows us to find solutions that satisfy both equations. Okay, so let's sub equation one into equation two. So we have 51 X minus is equal to three times why? So in this case three times 17 x minus 51 expanding on the right hand side, we get 51 X -153. All right, well, that's the exact same thing we have on the left hand side. Okay, so we can subtract 51 X add 153 and you'll see that we get zero is equal to zero. Okay, well this is a true statement, zero is equal to zero and zero is always equal to zero. Okay? So it doesn't matter what X or Y. Value we put into this equation. This is going to be true. What this tells us is that we have infinitely many solutions. Okay. All right. And if we have infinitely many solutions, we want to write the solution as a set. Okay? So we want to write a set of points X and Y that satisfy these equations. Okay? And so when we're writing out the equation we want them to satisfy. We can choose either one of the equations we've been given. Okay, So we can use this first one. Why is equal to 17 X minus Or any multiple of it? That's going to give us all of the points that satisfy the system. Okay, so this is our answer. It's going to be the set of points X. Y. Such that Y is equal to 17 X -51. That is answer a I hope this video helped. Thanks everyone for watching

In Exercises 31–42, 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. y = 3x - 5 21x - 35 = 7y

Key Concepts

Solving Systems of Linear Equations

Identifying No Solution and Infinite Solutions

Expressing Solution Sets Using Set Notation

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