Question 13 Write an equation of a line passing through the point representing solution of the pair of linear equations x + y = 2 and 2x – y = 1, how many such lines can we find?
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Solution
Now, x+y = 2 ⇒ y = 2 – x if x = 0, then y = 2 and if x = 2, then y = 0 X02Y20PointsaB and 2x – y – 1 = 0 ⇒ y = 2x – 1 if x = 0, then y = -1 , if x = 12 , then y = 0 and if x = 1, then y = 1 X0121Y−101PointsCDE Plotting the points A (2,0), we get the straight line AB. Ploting the points c (0, - 1) and (12, 0), we get the straight line CD. The lines AB and CD intersect at E (1, 1). Hence, infinite lines can pass through the intersection point of linear equations x + y = 2 and 2x – y = 1 i.e., E (1,1) like as y = x, 2x + y = 3, x + 2y = 3 so on.