Question

Assertion: The graph of the two linear equations x - 2y = 1 and 2x + 3y = 9 intersect at (3, 1).

Reason: Every point lying on x - 2y = 1 is a solution of 2x + 3y = 9

Now, choose the correct option.

• A. Both the assertion and the reason are true and the reason is the correct explanation for the assertion.
• B. Both the assertion and the reason are true but the reason is not the correct explanation for the assertion.
• C. Assertion is true but the reason is false.
• D. If assertion is false but reason is true.

Answer 1

The correct option is C Assertion is true but the reason is false.

If (3,1) lies on the graph of x-2y=1 and 2x+3y=9, then (3,1) is a solution of x - 2y =1 as well as 2x + 3y=9.

Given,$x=3andy=1$

$x-2y=3-2\times 1=3-2=1$

Also, $2x+3y=2\times 3+3\times 1=6+3=9$

Thus, (3,1) lies on both $x-2y=1and2x+3y=9$
which means $x-2y=1$ and $2x+3y=9$ intersect at (3,1)

The reason states that every point on $x-2y=1$ lies on $2x+3y=9$
$(-1,-1)$ lies on $x-2y=1$ as $-1-2\times -1=-1+2=1$
$2\times -1+3\times -1=-2-3=-5\ne 9$
Thus, (-1,-1) does not lie on $2x+3y=9$

Hence, the reason is false.