SOLUTION: how do u slove linear systems by graphing?

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Question 179: how do u slove linear systems by graphing?
Answer by KMST(5484) About Me  (Show Source):
You can put this solution on YOUR website!
I don't solve linear systems by graphing, because I do not use a graphing calculator,
and I am likely to find the solution faster and easier by another "method",
Not all systems of equations can be easily graphed by human hands.
If I successfully graphed that system, the graph may not help solve the system, as in the case below:
system%284x%2B2y=3%2C5y-4x=20%29
If I graph 4x%2B27=3 and 5y-4x=20%29 ,
I get this: The solution is the set of coordinates of the intersection point, but what are those coordinates?
Maybe x=-0.9 and y=3.3 ?
If a graphing calculator did it for me and told me the solution with more decimal places, I would ask it to express it as a fraction with a denominator of up to 2 digits.
Then, I would get highlight%28system+%28x=-25%2F28%2Cy=23%2F7%29%29 as the solution.
My estimates were very close, but there is no way that I could have estimated that set of values from the my hand-drawn graph.

HOW TO SOLVE A SYTEM OF LINEAR EQUATIONS BY GRAPHING:
If you were given a problem to solve by graphing, and a graphing calculator was not needed,
the step would be
1. Graph each linear equation.
2. If they both graph as the same line, the system has infinite solutions.
3. If both lines are parallel, the system has no solutions, but make sure they really are parallel. for a trick question, you could have given a problem where the lines just look parallel to some.
4. If the lines intersect, estimate the coordinates of the intersection point.
5. Verify your estimate is correct by substituting the coordinate values into both equations.
EXAMPLE:
system%28green%284x-3y=10%29%2Cred%283x%2B4y=20%29%29
1. My graph would be:
2. The two linear equations do no both graph as the same line, so we go to step 3.
3. Both lines are obviously not parallel, so we go to step 4.
4. The lines intersect, and my estimate for the coordinates of the intersection point are system%28x=4%2Cy=2%29 ,
but I must go to step 5.
5. Verifying my estimated solution :
For system%28x=4%2Cy=2%29 , system%28green%284x-3y%29=4%2A4-3%2A2=16-6=0%2Cred%283x%2B4y%29=3%2A4%2B4%2A2=12%2B8=20%29
The estimated values make both equations true, so the solution to the system is highlight%28system%28x=4%2Cy=2%29%29 .

Easy, right? The hard part that I did not show is graphing each linear equation.
You only need the coordinates of two points, right?
Two points that are close together may cause your drawn line to be off far outside those points.
How do you find two good points?