Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Consider the system of equations:
-2x + Ky = 26
13x - 6у = -7
Find all values of k for which the system has exactly one solution. Choose "does not exist" if such a k does not exist.

Sagot :

kevinclq0811

Answer:

Step-by-step explanation:

First of all, if the system of equations has exactly one solution, then the graph of these two equations will intersect at exactly one point, which means their slopes will be different. If the slopes are the same, there could be infinitely many solutions or no solution.

Rearrange the first equation to solve for slope of  [tex]-2x+ky=26[/tex]

y = (2/k)x + 26/k

The slope is 2/k.

The slope of the second equation is 13/6

as long as 2/k does not equal to 13/6, we have exactly one solution.

SO, the last step:

[tex]\dfrac{2}{k} \neq \dfrac{13}{6}\\[/tex]

[tex]k \neq \dfrac{2}{\dfrac{13}{6}}[/tex]

[tex]k\neq \dfrac{12}{13}[/tex]

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.