Can someone help me solve these graph problems?

Question

4x - 6y = 2 and 2x - 3y = 1

Answer 1

It depends on what the question is. If it's point of intersection, it will be:

4x-6y=2 (eqn 1.)

2x-3y=1 (eqn. 2)

Rearrange so x is the main unknown.

x=(1-3y)/2 (this would be eqn. 3)

So sub (eqn 3) into (eqn.1)

4[(1-3y)/2]-6y=2

Simplify it down to this:

2(1-3y)-6y=2

2-6y=2

6y=4

y=4/6

y=2/3

Then sub y=2/3 into (eqn 2)

So then its:

2x-3(2/3)=1

2x-2=1

2x=3

x=3/2

Therefore point of intersection is: [(3/2), (2/3)]

Hope it helps!