Question

find the equation of a straight line through the intersection of lines 2x+y=3 & 5x+y=6and parallel to the lines 13x+5y+12=0​

Answer 1

Answer:

ANSWER

Consider the given equation of the line.

2x+y−3=0 ...........(1)

5x+y−6=0 ...........(2)

(2)−(1)

5x−2x+y−y−6+3=0

⇒3x−3=0

⇒x=1 sun in (1)

2(1)+y−3=0

y−1=0

y=1

⇒Point of intersection of above both lines is

=(1,1)

Given points

A(1,2),B(2,1)

Slope of AB=

2−1

1−2

=

1

−1

=−1

Since, the line is parallel to the the line AB, so the slope must be equal.

So, the equation of line passes through intersection point

y−1=−1(x−1)

y−1=−x+1

x+y−2=0

Hence, this is the answer.

Step-by-step explanation:

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