Question : If the graph of the equations $x+y=0$ and $5y+7x=24$ intersect at $m,n$, then the value of $m+n$ is:
Option 1: 2
Option 2: 1
Option 3: 0
Option 4: –1
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Correct Answer: 0
Solution :
Given: $x+y=0$ and $5y+7x=24$
From the first equation, we have $y=-x$.
Putting the value of $y$, we get:
$5(-x) + 7x = 24$
⇒ $2x = 24$
$\therefore x = 12$.
Putting $x = 12$ into the first equation
Then, $y = -12$.
Thus, the point of intersection $(m,n)$ is $(12, -12)$.
So, $m+n=12 + (-12) = 0$.
Hence, the correct answer is 0.
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