SOLUTION: could someone give me a hand with this I can't quite wrap my head around it. 4x+y=6 , x+y=3 any help you can give would be appreciated

Question 972509: could someone give me a hand with this I can't quite wrap my head around it.
4x+y=6 , x+y=3
any help you can give would be appreciated
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!

4x+y =6
x +y =3
------------- Subtract
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

....eq.1
....eq.2
here you are given two equations of a line and you need to solve it as a system
that means these two lines might have intersection point in common, or they might have not common point at all ( in other words, they can be parallel), or they can have all points in common ( in other words, they can lie on top of each other, or simply be same line)
to find solution, you can decide whether you would use the graphing, substitution, or elimination method to solve the following system of equations
it would be much easier to use the elimination method in this case because you can easily eliminate
....eq.1
....eq.2
-------------------------subtract eq.2 from eq.1

now, go back to eq.1 or eq.2, plug in for and solve for :

....eq.2

so, now we know that both lines intersect in one point which has coordinates and
(,)-intersection point
we can check it on a graph:

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