For this set of simultaneous equations: (m-3)x+8y=10 and 5x+(m+3)y=11, find the values of m for which the solutions have: no solutions, unique solutions and infinite solutions.

Question

anonymous · Answer

I have found that the values for m are 7 and -7 by substitution and then equating co-efficients.

anonymous · Answer

* no solutions, unique solutions and infinite solutions. The key is first understanding what those terms mean.

anonymous · Answer

I do. No solutions means that the graphs don't intersect; unique solutions means that there is a set amount of solutions and infinite solutions means that there are a LOT of solutions.

anonymous · Answer

I got the solutions for m and I don't know what do with them.

anonymous · Answer

If you try to solve in terms of m, you will get
$$
\left(
\begin{array}{cc}
 x=\frac{2 (5 m-29)}{m^2-49} &
   y=-\frac{83-11 m}{m^2-49} \
\end{array}
\right)\
m=\pm 7\implies  \text {no  solution}
$$

anonymous · Answer

I got those answers, except I don't know how to put them into the form the question asks.

anonymous · Answer

$$
m=\pm 7\implies  \text{no solutions}\
m\ne \pm 7\implies \text{  unique solution}\
m=\frac{47}4 \implies  \text{ double solution }
$$

anonymous · Answer

Where did you get the 47/4?