# If the straight line passes through the point of intersection of the lines x + y = 3 and 2x – 3y = 1 and is parallel to x – y – 6 = 0, find a and b.

Given: lines are x + y = 3 and 2x − 3y = 1.

To find:

a and b.

Concept Used:

Point of intersection of two lines.

Explanation:

x + y − 3 = 0 … (1)

2x − 3y − 1 = 0 … (2)

Solving (1) and (2) using cross - multiplication method:

x = 2 , y = 1

Thus, the point of intersection of the given lines is (2, 1).

It is given that the line passes through (2, 1).

……(3)

It is also given that the line is parallel to the line x − y − 6 = 0.

Hence, Slope of is equal to the slope of x − y − 6 = 0 or, y = x – 6

- b/a = 1

b = - a … (4)

From (3) and (4):

a = 1

From (4):

b = −1

a = 1,

b = −1

Hence, a = 1, b = - 1

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