Determine the constant k so that the system of linear equations has infinitely many solutions
Video TranscriptHello. Our question says that linear equations two x minus three Y equal to eight and minus of four X plus six Y equals to k determine the constant case. So that the system has infinitely many solutions. So we are given with linear equations two X- of three Y equals to it. Then another equation is minus of four X plus of six Y equals to k determined the constant K. So that the system of equations is infinitely many solutions. Just so just see that I'll be writing a concept here. Evan, X plus B one, Y plus seven equals to zero and then a two X plus B. Two, Y Plus C2 equals to zero. So if you need to write about infinitely many solutions in finite Lee many solutions. So to have infinitely many solutions you must have the ratio of coefficients. Even by a two equals two. B one baby two. And then constant this condition. Alright, so I'll be writing this year to buy minus four equals two minus of three. Basics request to add bacon. Alright, so there's there's no problem if you do not right here as a minus set and here as a minus case. Still you will be writing minus and minus. Can that will be a positive. Right, So now further you can write that this is -1x2. This is also minus of one. Maybe 2. If you cancel all this and then add baking. So by last two or first and last. Still you will be solving this. So you'll be writing minus K. Close to 16. So K is going to be equal to negative of 16, So value of K is going to be equal to negative of 16. And I hope this answered your questions. Thank you. Show
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Mahra A. 8x+9y=72 x+ky=9 Determine the value of k for which the system of linear equation has infinitely many solutions. Then find all solutions corresponding to this value of K 2 Answers By Expert Tutors
Hi! It will have infinitely many solutions if one of the equations is equal to (the other one times a factor). 8x+9y=72 is eight (factor) times bigger than x+ky=9 (I know that because I know that 72 is eight times bigger than 9). Just like 72:8=9, you can say that 9:8=k That’s your answer!! K=9/8 yay!!! 🤩🤩🤩
Destiny M. answered • 05/26/19 Math Major; English and Math Tutor In order for the system of equations to have infinitely many solutions, x + ky = 9 must be equivalent to 8x+9y=72. Multiplying the second equation by 8: 8(x + ky = 9) Distributing the 8: 8x +8ky = 72 Now we need 9 to be equivalent to 8k in order for the system to be equivalent. In order to see what value of k would make 9 and 8k equivalent, we set them equal to each other. 9 = 8k Divide both sides by 8: k = 9/8 Therefore , in order for the system of equations to have infinitely many solutions, k must be 9/8 Still looking for help? Get the right answer, fast.ORFind an Online Tutor Now Choose an expert and meet online. No packages or subscriptions, pay only for the time you need. For what value S of K will the system have infinitely many solutions?(2) Infinitely many solutions occurs for no value of k.
How can you tell if a linear system has infinitely many solutions?A system of linear equations has infinite solutions when the graphs are the exact same line.
For what values of k will the following pair of linear equations have infinitely many solutions?For what values of k will the following pair of linear equations have infinitely many solutions? kx + 3y - (k – 3) = 0. 12x + ky - k = 0. The value of k which satisfies both the equations is 6.
What value of k will the system have no solutions?Hence, the given system of equations will have no solution, if k=2.
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