Solve using substitution:
show work

2x + 5y = -5
x + 3y = 3

answer:

{x,y} = {-6/11,9/11}

step-by-step explanation:

[1]     2x + 5y = 3

  [2]     -x + 3y = 3

// solve equation [2] for the variable   x  

  [2]     x = 3y - 3

// plug this in for variable   x   in equation [1]

  [1]     2•(3y-3) + 5y = 3

  [1]     11y = 9

// solve equation [1] for the variable   y  

  [1]     11y = 9  

  [1]     y = 9/11  

// by now we know this much :

    x = 3y-3

    y = 9/11

// use the   y   value to solve for   x  

    x = 3(9/11)-3 = -6/11

solution :

{x,y} = {-6/11,9/11}

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step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.