Question

(b) Find the point midway between the point (-1, 3) and the point of intersection of the lines
4x + y = 10 and 2x + 3y = 8.

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Answer 1

Answer:

Let the equation of the line having equal intercepts on the axes be

a

x

+

a

y

=1

x+y=a....(1)

On solving equation 4x+7y−3=0 and 2x−3y+1=0 we obtain x=

13

1

andy=

13

5

∴{

13

1

,

13

5

} is the point of intersection of the two given lines.

Since equation (1) passes through point {

13

1

,

13

5

}

{

13

1

+

13

5

}=a

⇒a=

13

6

∴ Equation (1) becomes x+y=

13

6

,i.e.,13x+13y=6

Thus the required equation of the line is 13x+13y=6