Question

Find k, if the following equation are consistent 7x-ky=4,2x+5y=9,2x+y=8

Answer 1

See the above attached photo for the ans hope it helps you

Answer 2

System of equation

It is given that equations are consistent.

$7x-ky=4--------------(i)\\2x+5y=9-------------(ii)\\2x+y=8-------------(iii)$

A linear or nonlinear system of equations is said to be  consistent if there is at least one set of values for the unknowns that satisfies each equation in the system or  when substituted into each of the equations, they make each equation hold true as an identity.

On subtracting equation (iii) from equation (ii), we get,

$4y=1\\\implies y=\frac{1}{4}$

On putting the  value of y in equation (iii), we get,

$2x+\frac{1}{4}=8\\\\ \implies 2x=\frac{31}{4} \\\\\implies x=\frac{31}{8}$

On substituting the value of x and y in equation (i), we get,

$7(\frac{31}{8})-k(\frac{1}{4})=4\\ \\ \implies \frac{217}{8}-\frac{k}{4}=4\\ \\ \implies 217-2k=32\\\\\implies 185=2k\\\\\implies k=92.5$

Hence the value of k for which this system of equation is consistent is 92.5 or $\frac{185}{2}$.