Verify the following pair of linear equations are consistent/inconsistent ? 2x – 2y – 3 = 0, 4x – 4y – 6 = 0
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(i) x+y=5 ...(i)
2x+2y=10 ...(ii)
⇒x+y=5
⇒y=5−x
x 0 3 y 5 2Plot (0,5) and (3,5) on graph and join them to get equation x+y=5.
2x+2y=10
⇒2y=(10−2x)
⇒y=210−2x=5−x ...(iii)
x 5 2 y 0 3
So, the equation is consistent and has infinitely many solution
(ii) x−y=8 ....(i)
3x−3y=16 ....(ii)
⇒x−y=8
⇒−x+y=−8
⇒y=−8+x
⇒y=x−8
x 8 0 y 0 -83x−3y=16 ...(ii)
⇒3x=16+3y
⇒3x−16=3y
⇒y=33x−16⇒y=x−316
x 316 0 y 0
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