Home > Geometry calculators > Coordinate Geometry > Find the equation of a line passing through point of intersection of the lines 5x+2y-11=0 and 3x-y+11=0 and it is parallel to 4x-3y+2=0

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 Find line through intersection point of 5x+2y-11=0, 3x-y+11=0, parallel to 4x-3y+2=0 [ Calculator, Method and examples ]Solution:Your problem -> line through intersection point of 5x+2y-11=0, 3x-y+11=0, parallel to 4x-3y+2=0The point of intersection of the lines can be obtainted by solving the given equations.5x+2y-11=0:.5x+2y=11and 3x-y+11=0:.3x-y=-115x+2y=11 ->(1)3x-y=-11 ->(2)equation(1) xx 1 =>5x+2y=11equation(2) xx 2 =>6x-2y=-22Adding =>11x=-11=>x=-11/11=>x=-1Putting x=-1 in equation (2), we have3(-1)-y=-11=>-y=-11+3=>-y=-8=>y=8:. x=-1" and "y=8:. (-1,8) is the intersection point of the given two lines.4x-3y+2=0:. 3y=4x+2:. y=(4x)/(3)+2/3:. Slope=4/3:. Slope of parallel line=4/3The equation of a line with slope m and passing through (x_1,y_1) is y-y_1=m(x-x_1)Putting (-1,8) for (x_1,y_1) and m=4/3, we get:. y-8=4/3(x+1):. 3(y-8)=4(x+1):. 3y -24=4x +4:. 4x-3y+28=0

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