How do you find the point of intersection for 3x-y=4 and 6x+2y= -8?

1 Answer
Jul 4, 2015

Intersection point : (0,-4)

Explanation:

We want to find the point A(X,Y) like :
3X-Y=4 and 6X+2Y=-8

The word "intersection", here, is referring to functions :
A function is generally writing : y=f(x)

Then, we need to transform the two equations to something like :
"y=..."
Let's define functions f,g, who are respectively representing equations 3x-y=4 and 6x+2y=-8

Function f :
3x - y = 4 <=> 3x = 4 + y <=> 3x-4 = y
Then we have f(x)=3x-4

Function g :
6x + 2y = -8 <=> 2y = -8 - 6x <=> y= -4-3x
Then we have g(x)=-3x-4

A(X,Y) is an intersection point between f and g then :
f(X) = Y and g(X)=Y
We can mark here f(X) = g(X) and more :

3X-4 = -3X-4
<=> 3X = -3X (we added 4 to each side)
<=> 6X = 0
<=> X = 0

Then : A(0,Y) and Y=f(0)=g(0)=-4

The coordinates of A is A(0,-4)

We can check the result with a graph of the situation (Alone, this is not a proof !!)

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