Check whether the following equations are consistent or inconsistent , solve them graphically.
2x + y - 6 = 0 and 4x - 2y -4 = 0

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Solution

2x + y - 6 = 0 and 4x - 2y -4 = 0
$\frac{a_{1}}{a_{2}} = \frac{2}{4} = \frac{1}{2}, \frac{b_{1}}{b_{2}} = \frac{1}{- 2} \frac{c_{1}}{c_{2}} = \frac{- 6}{- 4} = \frac{3}{2}$
$∴ \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
$∴$ the linear equation are consistent
$∴$ They have infinity solutions.
2x + y = 6 4x - 2y = 4
x y (x ,y) x y (x,y)
3 0 (0,6) 0 2 (0,-2)

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2x + y - 6 = 0, 4x - 2y - 4 = 0

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Check whether the following equations are consistent or inconsistent , solve them graphically.2x + y - 6 = 0 and 4x - 2y -4 = 0

2x + y - 6 = 0 and 4x - 2y -4 = 0a1a2=24=12,b1b2=1−2c1c2=−6−4=32∴a1a2≠b1b2∴ the linear equation are consistent ∴ They have infinity solutions.2x + y = 6 4x - 2y = 4 x y (x ,y) x y (x,y) 3 0 (0,6) 0 2 (0,-2)

Check whether the following equations are consistent or inconsistent , solve them graphically.
2x + y - 6 = 0 and 4x - 2y -4 = 0