Home > Geometry calculators > Coordinate Geometry > Find the equation of a line passing through point of intersection of lines 4x+5y+7=0 and 3x-2y-12=0 and point A(3,1)

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 Problem: line through intersection point of 4x+5y+7=0, 3x-2y-12=0 and (3,1) [ Calculator, Method and examples ]Solution:Your problem -> line through intersection point of 4x+5y+7=0, 3x-2y-12=0 and (3,1)The point of intersection of the lines can be obtainted by solving the given equations.4x+5y+7=0:.4x+5y=-7and 3x-2y-12=0:.3x-2y=124x+5y=-7 ->(1)3x-2y=12 ->(2)equation(1) xx 2 =>8x+10y=-14equation(2) xx 5 =>15x-10y=60Adding =>23x=46=>x=46/23=>x=2Putting x=2 in equation (2), we have3(2)-2y=12=>-2y=12-6=>-2y=6=>y=-3:. x=2" and "y=-3:. (2,-3) is the intersection point of the given two lines.Here A(3,1), (2,-3) are the given points:. x_1=3, y_1=1, x_2=2, y_2=-3The equation of a line AB is(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1):. (y-1)/(-3-1)=(x-3)/(2-3):. (y-1)/(-4)=(x-3)/(-1):. -(y-1)=-4(x-3):. -y +1=-4x +12:. 4x-y-11=0

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