Home > Geometry calculators > Coordinate Geometry > Find the equation of a line passing through point of intersection of lines 2x+3y+4=0 and 3x+6y-8=0 and having slope = 2

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 Problem: line through intersection point of 2x+3y+4=0, 3x+6y-8=0 and slope=2 [ Calculator, Method and examples ]Solution:Your problem -> line through intersection point of 2x+3y+4=0, 3x+6y-8=0 and slope=2The point of intersection of the lines can be obtainted by solving the given equations.2x+3y+4=0:.2x+3y=-4and 3x+6y-8=0:.3x+6y=82x+3y=-4 ->(1)3x+6y=8 ->(2)equation(1) xx 3 =>6x+9y=-12equation(2) xx 2 =>6x+12y=16Substracting =>-3y=-28=>3y=28=>y=28/3Putting y=28/3  in equation (1), we have2x+3(28/3)=-4=>2x=-4-28=>2x=-32=>x=-16:. x=-16" and "y=28/3:. (-16,9.33) is the intersection point of the given two lines.The equation of a line with slope m and passing through (x_1,y_1) is y-y_1=m(x-x_1)Putting (-16,9.33) for (x_1,y_1) and m=2, we get:. y-9.3333=2(x+16):. (y-9.3333)=2(x+16):. y -9.3333=2x +32:. 2x-y+41.3333=0

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