Heyy, I don't know if there is already a math method discussion forum
i wanted to ask, how do we find out the value of m for which the simultaneous linear equations (m-3)x+8y=10 and 5x+(m+3)y=11 has a unique solution?
I've looked in the textbook but the example and explanation that they give is really limited
any help is appreciated TYSM!
a unique solution means that both lines intersect at only one distinct point. Imagine this in you head and you will release that the slope (gradient) will always have to be different.
solve both of the equations for y (so that you get smth like y=). Equate the gradients and find the value of m for which the equation holds true. Let's say when m=1, the gradients are equal. Then when m is an element of all real numbers except 1, the gradients will not be equal.
Thus our answer will be m∈R{1}. I havent actually solved the equation for myself, so idk if its 1, but I'll leave that to you.
If my explanation was not clear enough or you still have questions, shoot me a reply.
That's right, the CAS has many shortcuts that will save heaps of time. However I do suggest you to learn the tech-free method as it may appear in a SAC as it did for me. It is also possible that it appears in the Exam 1. Definitely use the CAS program for MCQ's tho.
