It is not possible to solve a single linear equation in two unknown variables.
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x=4, y=9 (4,9)
If 8x + 4y = 16, then y = - 2x + 4 Thus the slope is -2 and the intercept is 4.
-8x + 4y = 28 Add 8x to each side: 4y = 8x + 28 Divide both sides by 4: y = 2x + 7
Equations: y = x+4 and x^2 +y^2 -8x +4y = 30 It appears that the given line is a tangent line to the given circle and the point of contact works out as (-1, 3)
They are perpendicular lines because the slopes are 3/4 and -4/3 respectively.