Intersection of Two Lines

Question

a(1−ax)=y
2(ax−y)+1=−3(x+y)

 

I need to find the Intersection of these two lines
Thanks for the help!

 

The answer is: (1/a-3 , 3a/3-a) but I can't get to it 

Answer 1

Noel,

 

Where you see "a" plug in a number - any number - and you will see that it's a straightforward case of simultaneous equation, e.g. 3(1-3x)=y and 2(3x-y)=-3(x+y) <=> -9x-y=-3 and 6x-2y=-3x-3y <=> ........

 

Back t the equation with "a"

 

a - a²x = y and 2ax - 2y + 1 = -3x - 3y

 

<=> a²x + y = a and -(2a + 3)x - y = -1

 

Now add the two equations and that will eliminate y 

 

[a² - (2a + 3)]x = a -1

 

x = (a -1)/(a² - (2a + 3) 

 

Substitute this a value in one of the two equations and solve for y

 

Now set the quadratic equation a² - (2a = 3) = 0 and solve for "a" so you can exclude that value of a from the domain.

I hope this helps