Question 1 Graphically, solve the following pair of equations 2x + y = 6 and 2x – y + 2 = 0 Find the ratio of the areas of the two triangles formed by the lines representing these equations with the X-axis and the lines with the y-axis.
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Solution
Given equation are 2x + y = 65 and 2x – y + 2 = 0 Table for equation 2x + y = 6 X03Y60PointsBA Table for equation 2x – y + 2 = 0 X0−1Y20PointsDC Let A1andA2 represent the areas of DeltaACEandΔBDE, respectively
Now,A1=AreaofΔACE=12×AC×PE=12×4×4=8andA2=AreaofΔBDE=12×BD×QE=12×4×1=2∴A1A2=8:2=4:1 Hence, the pair of equations intersect graphically at point E (1, 4) i.e., x = 1 and y = 4