Mathematics

Equation of the line passing through the point of intersection of the lines $$2x+3y-5=0, 3x+2y-5=0$$ and having slope $$-1$$ is 


SOLUTION

We have

Equation of lines

 

$$ 2x+3y-5=0\ ......\ \ (1) $$

$$ 3x+2y-5=0\ \ ......\ \ (2) $$

 

On solving equation $$(1)$$ and  $$(2)$$ to,

$$(x,\ y)\ $$=$$\ (4,\ 1)$$


Let the intersection point

$$(x_1,\ y_1)$$$$\ =$$$$\ (4,\ 1)$$


Given that

The slope of line $$(m)\ =\ -1$$

So,

Equation of line

 $$ y-{{y}_{1}}=m(x-{{x}_{1}}) $$

$$ y-1=-1(x-4) $$

$$ y-1=-x+4 $$

$$ x+y-5=0 $$


Hence, this is the answer.

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