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{{:(5x-3y=10),(6y=kx-42):} In the system of linear equations above, k represents a constant. If the system of equations has no solution, what is the value of 2k? |
Answer» <html><body><p>`5/2`<br/>5<br/>10<br/>20</p>Solution :Start by recognizing that for two lines to be parallel, the coefficients for x must be identical in the two equations, dutto for the coefficients for y. Manipulate the second <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> so that it is in the same format as the first one: <br/> `kx - 6y=42` <br/> The y-coefficient in the first equation, `5x-3y=10, is <a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>.` Divide the second equation by 2 in <a href="https://interviewquestions.tuteehub.com/tag/order-1138220" style="font-weight:bold;" target="_blank" title="Click to know more about ORDER">ORDER</a> to make the y-coefficients in both equatinos equal: <br/> `k/2x -3y=21` <br/> Now set the x-coefficient equal to the x-coefficient in the first equation: <br/> ` k /2=5` <br/> `k=10` <br/> Note that the question asks for the value of <a href="https://interviewquestions.tuteehub.com/tag/2k-300402" style="font-weight:bold;" target="_blank" title="Click to know more about 2K">2K</a>, so the correct answer is (D), 20.</body></html> | |