Find the value of m for which the simultaneous equations
(m + 3)x + my = 12
(m + 1)x + (m - 3)y = 7
have no solution.
I am insure what to do here! Do I need to set them up in a matrix or...
Any help would be appreciated! Thanks
There will not be a solution if the two linear equations are parallel.
Rewrite them in $\displaystyle y = ax + b$ form.
$\displaystyle y = -\frac{m + 3}{m}x + \frac{12}{m}$
$\displaystyle y = -\frac{m + 1}{m - 3}x + \frac{7}{m - 3}$.
Since they are parallel, the gradients are the same.
So $\displaystyle -\frac{m + 3}{m} = -\frac{m + 1}{m - 3}$
$\displaystyle (m + 3)(m - 3) = m(m + 1)$
$\displaystyle m^2 - 9 = m^2 + m$
$\displaystyle m = -9$.