Q5 of 92 Page 64

Tathagata has written a linear equation in two variables x + y = 5. I write another linear equation in two variables, so that, the graphs of two equations will be

intersecting

x + y = 5 …(1)

Let us express the equations (1) in the form of


a1x + b1y + c1 = 0 where a and b can’t be 0 at the same time.


Let the required equation be a2x + b2y + c2 = 0


x + y = 5


∴ x + y + (-5) = 0


Or 1 × x + 1 × y + (-5) = 0


Here a1 = 1, b1 = 1, c1 = -5


For lines of equation to be intersecting in the graph, we need



Let , and c1 = c2 where k1 and k2 are any real number


and k1≠k2 also both are non zero.


For simplicity, take k1 = 0.5 and k2 = 0.2


So, , and



Therefore, required equation is 2x + 5y – 5 = 0 which will be intersecting in the graph with equation x + y = 5


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