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show that the straight lines represented by the equations 3x+y+5=0 , 3y-x=5 and 2x+5y=1 are concurrent and find the coordinates of the point where they intersect.

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We have,3x+y+5=0                           .....i3y-x=5 or x-3y+5=0  .....ii2x+5y=1                               .....iiii×3+ii9x+3y+15+x-3y+5=0⇒10x+20=0⇒x=-2010⇒x=-2Substituing x=-2 in i, we get3-2+y+5=0⇒-6+y+5=0⇒y=1Substituting x=-2 and y=1 in LHS of i, we getLHS=2x+5y=2-2+51=-4+5=1=RHSHence, all the three lines are concurrent and the intersecting point is -2,1.

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If the line 4x+5y = 30 cut the x−axis then y = 0 4x+0 = 30 x = 304= 7.5So coordinate is (7.5,0)And when line 4x+5y = 30 cut the y−axis then x = 0 0+5y = 30 y =6 So coordinate is (0,6) 2)Line x= 4 is a line 4 unit away from the y −axis and parallel to y axis line y = 2 is a line parallel to x−axis and at a distance of 2 unit from positive y axisand y = x is a line which passes through the points like (1,1), (2,2), etcNow plotting them we get If the line 4x+5y = 30 cut the x-axis then y = 0 4x+0 = 30 x = 304= 7.5So coordinate is 7.5,0And when line 4x+5y = 30 cut the y-axis then x = 0 0+5y = 30 y =6 So coordinate is 0,6 2)Line x= 4 is a line 4 unit away from the y -axis and parallel to y axis line y = 2 is a line parallel to x-axis and at a distance of 2 unit from positive y axisand y = x is a line which passes through the points like 1,1, 2,2, etcNow plotting them we get


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