What are the variables if PT= 2x, TR= y+4, QT= x+2, TS=y
1 answer:
The missing aspect of this question is shown in the attached image, which is that the letters correspond to vertices of a parallelogram.
A key feature of the parallelogram is that the diagonals bisect each other, therefore:
PT = TR
QT = TS
With this information we can now plug in the equations and solve for the variables x and y.
PT = TR
2x = y+4
y = 2x - 4
QT = TS
x + 2 = y
We now have two equations for the variable y. With this we can solve for x.
2x - 4 = x + 2
x = 6
y = x + 2
y = 6 + 2
y = 8
Once we solved for the variable x, we simply placed that value back into one of the previous equations and solved for y. The results are x = 6, y = 8.
A key feature of the parallelogram is that the diagonals bisect each other, therefore:
PT = TR
QT = TS
With this information we can now plug in the equations and solve for the variables x and y.
PT = TR
2x = y+4
y = 2x - 4
QT = TS
x + 2 = y
We now have two equations for the variable y. With this we can solve for x.
2x - 4 = x + 2
x = 6
y = x + 2
y = 6 + 2
y = 8
Once we solved for the variable x, we simply placed that value back into one of the previous equations and solved for y. The results are x = 6, y = 8.
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