一道难题Whatvalueofmgivesasystemwithnosolution?x(m-1)-y+6=02x+y-3=0Howwouldyousolvethisquestion?Isthereawaytosolveitwithoutusingguessandcheck?Pleaseprovideadetailedanswer!Thankyou.

Question

一道难题
What value of m gives a system with no solution?
x(m-1) - y + 6=0
2x + y -3=0
How would you solve this question?Is there a way to solve it without using guess and check?Please provide a detailed answer!Thank you.

Answer 1

Solution:
This is a simultaneous equation.
Methods to solve simultaneous equation are:
1、Substitution；
2、Elimination；
3、Determinant；
4、Matrix
By Determinant method,
Δ = (m-1)×1 - (-1)×2 = m - 1 + 2 = m + 1
Let Δ = 0,ie.m + 1 = 0,m = -1
Graphical meaning::
-2x - y = -1 (Line L₁)
2x + y = 3 (Line L₂)
L₁// L₂
So,m = -1 means L₁is parallel to L₂(same gradient),no intersection.
Or:
Let L₁// L₂,we have -1/(m-1) = 1/2,so,m-1 = -2,m = -1