Solve the following pair of linear equations. 4x – 5y – 20 = 0 , 3x + 5y -15 = 0
2x-7y = 6 ….(i) 2x = 7y+6 x = (7y+6)/2 when y = 0 x = (7×0+6)/2 = 6/2 = 3 when y = -1 x = (7×-1+6)/2 = -1/2 = -0.5 when y = -2 x = (7×-2+6)/2 = -8/2 = -4 Mark the above points on the graph. Join them. 5x = 8y-4 x = (8y-4)/5 when y = 0 x = (8×0-4)/5 = -4/5 = 0.8 when y = 3 x = (8×3-4)/5 = (24-4)/5 = 20/5 = 4 when y = -2 x = (8×-2-4)/5 = (-16-4)/5 = -20/5 = -4 5x-8y = -4 …(ii) It is clear from the graph that the two lines intersect at (-4,-2). So the solution of the given equations are x = -4 and y = -2. Answer Verified
Hint: First draw the graph of the two given equations. To draw the graph of a straight line, we need at least two points. So, choose one of the equations and substitute x = 0, determine y, then substitute y = 0, determine x. Now, apply the same process for the second equation. Plot the graph of the two equations using the points obtained. Now, if the graphs of these equations are parallel but not coincident to each other then the system of equations is inconsistent. In case the graphs are
coincident or overlapped then there will be infinitely many solutions. Complete step-by-step answer: Clearly, we can see that the two lines are parallel to each other and do not intersect at any point. Hence, the system of equations is inconsistent (i.e. has no solution). Note: There is another method to check the consistency or inconsistency of a system of equations without the use of graphs. To apply this method, write the two equations in the form: ${{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0$ and ${{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0$ respectively. Now, consider the ratios: $\dfrac{{{a}_{1}}}{{{a}_{2}}},\dfrac{{{b}_{1}}}{{{b}_{2}}}\text{ and }\dfrac{{{c}_{1}}}{{{c}_{2}}}$. From here,
three cases can arise:
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