Question

For what value of k do the equations 5x-2y+8=0 & 15x+ky=-24​

Answer 1

Answer:

$solve\:for\:x,\:5x-2y+8=0\quad :\quad x=\frac{2y-8}{5}$

Step-by-step explanation:

$5x-2y+8=0$

$\mathrm{Add\:}2y\mathrm{\:to\:both\:sides}$

$5x-2y+8+2y=0+2y$

$5x+8=2y$

$\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}$

$5x+8-8=2y-8$

$5x=2y-8$

$x=\frac{2y-8}{5}$

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$solve\:for\:x,\:15x+ky=-24\quad :\quad x=\frac{-24-ky}{15}$

$15x+ky=-24$

$\mathrm{Subtract\:}ky\mathrm{\:from\:both\:sides}$

$15x+ky-ky=-24-ky$

$15x=-24-ky$

$\mathrm{Divide\:both\:sides\:by\:}15$

$\frac{15x}{15}=-\frac{24}{15}-\frac{ky}{15}$

$x=\frac{-24-ky}{15}$

Answer 2

Concept Introduction: Polynomial Equations are basic concepts of Mathematics.

Given:

We have been Given:

$5x - 2y + 8 = 0 \\ 15x + ky + 24 = 0$

To Find:

We have to Find: The value of k.

Solution:

According to the problem,

$a1 = 5 \\ a2 = 15 \\ b1 = - 2 \\ b2 = k \\c1 = 8 \\ c2 = 24$

therefore,

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} \\ \frac{5}{15} = \frac{ -2}{k} = \frac{8}{24} \\ 5k = - 30 \\ k = \frac{ - 30}{5} \\ k = - 6$

Final Answer: The value of k is

$k = - 6$

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