# Simultaneous equations

• Jan 7th 2010, 05:29 PM
scubasteve94
Simultaneous equations
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
• Jan 7th 2010, 05:57 PM
Prove It
Quote:

Originally Posted by scubasteve94
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 $\displaystyle -\frac{m + 3}{m} = -\frac{m + 1}{m - 3}$

$\displaystyle (m + 3)(m - 3) = m(m + 1)$

$\displaystyle m^2 - 9 = m^2 + m$

$\displaystyle m = -9$.