Question 617760: How do I solve 3x + y = -8
2x -y = -8 by graphing?
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How do I solve 3x + y = -8
2x -y = -8 by graphing?
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You graph the 2 equations.
Where they intersect is the x,y combination that fits both equations.
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! I suspect that you have a typo in your problem, because the solution does not involve whole numbers, as I would expect from that type of problem.
Otherwise, maybe you are expected to use a graphing calculator.
I cannot explain graphing calculators through this website.
I will solve the problem as posted, graphing the old way, by hand.
It will show you strategies to do that kind of solving, even if there was a typo.
To graph each line you need 2 points.
You chose the points aiming for easy calculations and a nice looking graph.
For easiest calculations, I would set x=0 and x=-5 and solve for y.
(Zeros are usually good choices, and I picked x=-5 because I saw it would give y values that would not be too large).
For equation 3x + y = -8:
x=0 --> y=-8 (That gives us point (0,-8)).
x=-5 --> 3(-5)+y=-8 --> -15+y=-8 --> y=-8+15 --> y=7 for point (-5,7)
For equation 2x - y = -8:
x=0 --> -y=-8 --> y=8
x=-5 --> 2(-5)-y=-8 --> -10-y=-8 --> -y=-8+10 --> -y=2 --> y=-2 for
Now, for each equation, we plot the points and connect them with a straight line.
 (The first equation is graphed in red, the second in blue, and the points are big circles).
In a typical problem of this type, the lines would cross at a point with integer x and y coordinates. You would read those coordinates from the graph, substitute in the equations and verifty that it is a solution.
Here they seen to cross at  or maybe  . This is not a typical problem and that is going to make calculations more cumbersome.
I checked x=-3.2 and got:
for equation 3x + y = -8, 3(-3.2)+y=-8 --> -9.6+y=-8 --> y=1.6
for equation 2x - y = -8, 2(-3.2)-y=-8 --> -6.4-y=-8 --> -y=-1.6 --> y=-1.6
So the lines really cross at the point with  and  , and that is the solution.
(I was betting on fifths because the slopes are 2 and 3, which adds to 5, and the equations could be the position of people walking towards each other at speeds of 2 miles and hour and 3 miles and hour, which would reduce the distance between them by 5 miles per hour).
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