Find the equation of straight line which passes through the point of intersection of straight lines. x+2y+3=0 and 3x+4y=7 and parallel to the straight line y-x=8

Equation of the line in question: .

Step-by-step explanation:

Start by finding the intersection of the two straight lines. The equation for both lines shall hold at their intersection. (Using the idea of the Gaussian Elimination.)

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Add -3 times the first equation to the second:

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Add the second equation to the first:

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Hence the intersection of the two lines will be .

Now, find the slope of that straight line. is equivalent to . The slope of that line is equal to 1. So will be the slope of the line in question.

Apply the point-slope form of a line on a Cartesian plane:

Equation of the line:

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Simplify to obtain:

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4444444444444 i think