Check whether the following equations are consistent or inconsistent , solve them graphically.
2x -2y -2 = 0 and 4x - 4y -5 =0

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Solution

2x -2y -2 = 0 and 4x - 4y -5 =0
$\frac{a_{1}}{a_{2}} = \frac{2}{4} = \frac{1}{2}, \frac{b_{1}}{b_{2}} = \frac{- 2}{- 4} = \frac{1}{2} = \frac{c_{1}}{c_{2}} = \frac{- 2}{- 5} = \frac{2}{5}$
$∴ \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
$∴$ the linear equation are consistent
$∴$ They have infinity solutions.
2x - 2y-2 = 0 4x - 4y -5 =0
x y (x ,y) x y (x,y)
0 -1 (0,-1) 2 $\frac{3}{4}$

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Check whether the following equations are consistent or inconsistent , solve them graphically.2x -2y -2 = 0 and 4x - 4y -5 =0

2x -2y -2 = 0 and 4x - 4y -5 =0a1a2=24=12,b1b2=−2−4=12=c1c2=−2−5=25∴a1a2=b1b2≠c1c2∴ the linear equation are consistent ∴ They have infinity solutions.2x - 2y-2 = 0 4x - 4y -5 =0 x y (x ,y) x y (x,y) 0 -1 (0,-1) 234

Check whether the following equations are consistent or inconsistent , solve them graphically.
2x -2y -2 = 0 and 4x - 4y -5 =0