compare the ratios of the coefficients and write whether the pair of equations 3x+4x-6=0and 4x-2y+3=0 is consistent or in consistent.
Answers
Answer:
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.
