Question 54109: Solve the system graphically.
2x+y=12
2x+y=22
please show me how to graph this
Found 2 solutions by stanbon, funmath:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1st: 2x+y=12
To graph this line you need two points:
Let x=0 then y=12 giving you the point (0.12)
Let y=0 the x=6 giving you the point (6,0)
Plot these two points on a coordinate system.
Draw a line through these two points.
That is your graph of this 1st line.
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2nd: 2x+y=22
Again:
Let x=0, then y=22 giving (0,22)
Let y=0, then x=11 giving (11,0)
Plot the points and draw the line.
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Comment: You should end up with two parallel lines.
Cheers,
Stan H.
Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website! Line 1) 2x+y=12
Line 2) 2x+y=22
This one has no solution, let me show you a quick way of seeing that. Put both equations in  form; where m=slope and (0,b)= y-intercept.
Line 1) 2x+y=12
Line 1) -2x+2x+y=-2x+12
Line 1) y=-2x+12
Line 2) 2x+y=22
Line 2) -2x+2x+y=-2x+22
Line 2) y=-2x+22
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So your 2 lines are:
y=-2x+12
y=-2x+22
Notice that both the m's are the same, m=-2 and the b's are different, 12 and 22 they are parallel lines that will never touch.
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Graphically:
Let x=10 for the 1st equation:
y=-2(10)+12
y=-20+12
y=-8
Plot (10,-8)
Let x=6 in the same equation:
y=-2(6)+12
y=-12+12
y=0
Plot (6,0)
Connect the dots.
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Let x=10 in the second equation.
y=-2(10)+22
y=-20+22
y=-2
Plot (10,-2)
Let x=6
y=-2(6)+22
y=-12+22
y=10
Plot (6,10)
Connect the dots.
This is what you get:
See they don't intersect. Therefore there's no solution!
Happy Calculating!!!
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