Find the value of 'k' for …
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Sia ? 6 years, 4 months ago
The given equations are
4x - 5y = k
So, 4x - 5y - k = 0......... (i)
And 2x - 3y = 12
So, 2x - 3y - 12 = 0 ......... (ii)
The system of linear equations is in the form of
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Compare (i) and (ii), we get
a1= 4 ,b1= -5, c1 = -k,
a2=2 ,b2= -3 ,c2 = -12
For a unique solution, we must have
{tex} \frac { a _ { 1 } } { a _ { 2 } } \neq \frac { b _ { 1 } } { b _ { 2 } }{/tex}
{tex}\frac { 4 } { 2 } \neq \frac { - 5 } { - 3 }{/tex}
{tex}2 \neq \frac { 5 } { 3 } \Rightarrow 6 \neq 5{/tex}
Thus, for all real value of k, the given system of equations will have a unique solution.
1Thank You