Question

are 3x+2y=5 and 2x-y=1 coincident or intersecting

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

pGiven pair of equations are :

2x + y - 5 = 0...........(1)

3x - 2y - 4 = 0.........(2)

from equation (1),

a_1=2,b_1=1,c_1=-5a

1

=2,b

1

=1,c

1

=−5

and from equation (2),

a_2=3,b_2=-2,c_2=-4a

2

=3,b

2

=−2,c

2

=−4

now, \frac{a_1}{a_2}=\frac{2}{3}

a

2

a

1

=

3

2

\frac{b_1}{b_2}=\frac{1}{-2}

b

2

b

1

=

−2

1

\frac{c_1}{c_2}=\frac{-5}{-4}=\frac{5}{4}

c

2

c

1

=

−4

−5

=

4

5

we see, \frac{b_1}{b_2}\neq\frac{c_1}{c_2}

b

2

b

1



=

c

2

c

1

hence, pair of equations represent intersecting.

now, multiplying 2 with equation (1) and adding with equation (2)

2(2x + y - 5) + (3x - 2y - 4) = 0

4x + 2y - 10 + 3x - 2y - 4 = 0

7x - 14 = 0 => x = 2

put x = 2 in equation (1),

2 × 2 + y - 5 = 0

y = 1

hence, x = 2 and y = 1

Step-by-step explanation:

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