Question 54109
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 {{{highlight(y=mx+b)}}} 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:
{{{graph(300,200,-10,10,-10,10,-2x+12,-2x+22)}}}
See they don't intersect.  Therefore there's no solution!
Happy Calculating!!!