Question

For what value of p and q for which system of equation represent coincident lines 2x+3y=7 and p(x+y)-q(x-y)=(3p+q-2)

Answer 1

Given: Two equations 2x + 3y = 7 and p(x+y) - q(x-y) = (3p+q-2)

To find: For what value of p and q for which system of equation represent coincident lines.

Solution:

• The equation p(x+y)-q(x-y)=(3p+q-2)  can be rewritten as

            px + py - qx + qy = 3p + q - 2

            x(p-q) + y(p+q) = 3p + q - 2

• Now as we know that the condition for coincident line is:

            a1/a2 = b1/b2 = c1/c2

• So writing the two two equations in above form, we get:

            2/p-q = 3/p+q = 7/3p+q-2

            from i and ii, we get:

            2/p-q = 3/p+q

            2(p+q) = 3(p-q)

            2p+2q = 3p-3q

            5q = p

            from ii and iii, we get:

            3/p+q = 7/3p+q-2

            9p+3q-6 = 7p+7q

            2p -4q = 6

• Putting value of p, we get:

            2(5q) - 4q = 6

            6q = 6

            q = 1

            p = 5(1) = 5

Answer:

              So the value of p and q are 5 and 1.