How many solutions does the system formed by x-y=3 and ax+3a=0 have for anon zero number a? Explain
Considering both equations x -y = 3, and ax + 3a = 0
ax + 3a = 0
ax = -3a Divide both sides by a, this is possible because a is non zero,
If it were zero we would have not being able to carry out the division process above because we would be dividing both sides by zero and that is undefined.
x = -3
From the second, x - y = 3, substitute the value of x = -3
-3 - y = 3
-y = 3 + 3
-y = 6
y = -6
Therefore for a non zero value of a, x = -3, y = -6. So the system of equations have 2 solutions.