While you cannot solve 946x+642y=911 for numerical values of x and y, you can indeed solve 946x+642y=911 first for x and then for y:
-911 - 642y
For x: 946x+642y=911 becomes 946x = 911 - 642y, or x = ------------------
946
911-946x
For y: 946x+642y=911 becomes 642y = 911-946x, or y = ---------------
642
Step-by-step explanation:
The one point where the lines intersect is one solution. If both points are on the same line it is one solution. If the lines do not intersect it is no solution.
Slope RS: 2/3
Slope ST: -3/2
Slope TU: 4/6 = 2/3
Slope UR: -1/5
Sides RS and TU have the same slope, so they are parallel.
The slope of side ST is the negative reciprocal of the slopes of sides RS and TU, so side ST is perpendicular to sides RS and TU.
Side UR is not parallel or perpendicular to any other side.
The quadrilateral is a trapezoid.
