Which of the following pair of equations are inconsistent? (a) 3x - y = 9,x - = 3 (c) 5x - y = 10, 10x - 2y = 20 (b) 4x + 3y = 24,- 2x + 3y = 6 (d) - 2x + y = 3.-4x + 2y = 10
Answers
Answer:
) 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 0y0−2Plot point (1,0) and (0,−2) on a graph and join them to get equation 4x−2y=0
x=2,y=2 is the solution of the given pairs of equation . So. solution is consistent.
(iv) 2x−2y=2 ...(i)
4x−4y=5 ...(ii)
2x−2y=2⇒2x−2=2y
y=x−1
x01y−10Plot point (0,1) and (1,0) and join to get the equation 2x−2y=2 on a graph 4x−4y=5⇒4x−5=4y
⇒44x−5=y
Plot point (0,6) and (3,0) on a graph and join then to get equation 3x+y=6
For equation (ii), 4x−2y=4⇒24x−4=y
x10y0−2Plot point (1,0) and (0,−2) on a graph and join them to get equation 4x−2y=0
x=2,y=2 is the solution of the given pairs of equation . So. solution is consistent.
(iv) 2x−2y=2 ...(i)
4x−4y=5 ...(ii)
2x−2y=2⇒2x−2=2y
y=x−1
x01y−10Plot point (0,1) and (1,0) and join to get the equation 2x−2y=2 on a graph
Answer:
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