SOLUTION: X= -3Y X+Y=4 SO WHAT POINT REPRESENTS THE COMMON SOLUTION FOR THE SYSTEM OF EQUATIONS? I know the answer is (6,-2), but how did they get that answer?

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: X= -3Y X+Y=4 SO WHAT POINT REPRESENTS THE COMMON SOLUTION FOR THE SYSTEM OF EQUATIONS? I know the answer is (6,-2), but how did they get that answer?       Log On


   

Question 192890: X= -3Y X+Y=4 SO WHAT POINT REPRESENTS THE COMMON SOLUTION FOR THE SYSTEM OF EQUATIONS? I know the answer is (6,-2), but how did they get that answer?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


EQN 1 : x = 3y

Via Slope-Intercept Form,system%28y=mx%2Bb%29
x=-3y
x%2F-3=cross%28-3%29y%2Fcross%28-3%29
red%28y=%28-1%2F3%29x%29


So the line has a Slope=m=-1%2F3=DELTA%28y%29%2FDELTA%28x%29
Since b=0, from the origin (0,0) --> one step down on y-axis(-1), then 3 steps right on x-axis(+3) for the next point.
---> point (3,-1)

From point (3,-1), move one step down on y-axis (-1), and 3 steps right on x-axis(+3):
---> Next point (6,-2)

Going back from the Origin (0,0), we move one step up on the y-axis(+1) and 3 steps to the left on x-axis(-3). this is to maintain our Slope=-1%2F3.
---> Next point (-3,1)

From point (-3,1), another one step up (+1) and 3 steps to the left(-3):
---> Next point (-6,2)

We connect the points for Line x=-3y




For the Next Line X+Y=4

Let Fy=0:
x%2By=4
x%2B%280%29=4 ---> red%28x=4%29, X-Intercept

Let Fx=0:
0%2By=4
red%28y=4%29 ,Y-Intercept

We see both Lines in the graph:
---> red%28RED=EQN1%29 intersects at point (6,-2) on green%28GREEN=EQN2%29

Thank you,
Jojo