Assertion: The linear equations 5x−2y−6=0 and 7x+5y−10=0 have exactly one solution. Reason: The linear equations 2x+3y−6=0 and 4x+6y−18=0 have a unique solution. *
2 points
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
Assertion is correct but Reason is incorrect.
Assertion is incorrect but Reason is correct
Answers
Step-by-step explanation:
x+y=5 ...(i)
2x+2y=10 ...(ii)
⇒x+y=5
⇒y=5−x
x 0 3
y 5 2
Plot (0,5) and (3,5) on graph and join them to get equation x+y=5.
2x+2y=10
⇒2y=(10−2x)
⇒y=
2
10−2x
=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 -8
3x−3y=16 ...(ii)
⇒3x=16+3y
⇒3x−16=3y
⇒y=
3
3x−16
⇒y=x−
3
16
x
3
16
0
y 0
3
−16
Plotting both the equation in graph, we see that the lines are parallel , so inconsistent.
(iii) 2x+y−6=0
4x−2y−4=0
2x+y=6 ....(i)
4x−2y=4 ...(ii)
For equation (i), 2x+y=6⇒y=6−2x
x 0 3
y 6 0
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⇒
2
4x−4
=y
x 1 0
y 0 −2
Plot 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
x 0 1
y −1 0
Plot point (0,1) and (1,0) and join to get the equation 2x−2y=2 on a graph 4x−4y=5⇒4x−5=4y
⇒
4
4x−5
=y
x 0
4
5
y −
4
5
0
Plot point (0,−
4
5
) and (
4
5
,0) and join them to get the equation 4x−4y=5 on a graph.
The two lines never intersect, so, the solution is inconsistent.