Answer:
14) x = 6 and y = 8
15) x = -1 and y = 1
16) x = 7 and y = 10
Step-by-step explanation:
14) From the given parallelogram, we can say that;
PT = TR and QT = QS due to the fact that the diagonals bisect each other into two equal parts.
Thus;
If PT = 2x, TR = y + 4, QT = x + 2, TS = y; then we have;
PT = TR
2x = y + 4
y = 2x - 4 - - - eq 1
Also;
QT = QS
x + 2 = y - - - eq 2
Put x + 2 for y in eq 1 to get:
x + 2 = 2x - 4
2x - x = 4 + 2
x = 6
Put 6 for x in eq 2 to get;
6 + 2 = y
y = 8
15) similarly from above;
x + 2 = y - - - eq 1
2x = y + 3
y = 2x + 3 - - - eq 2
Put 2x + 3 for y in eq 1;
x + 2 = 2x + 3
2x - x = 2 - 3
x = -1
Put -1 for x in eq 1 to gwt;
-1 + 2 = y
y = 1
16) similarly again;
y = x + 3 - - - (eq 1)
2y = 3x - 1 - - - (eq 2)
Put x + 3 for y in eq 2;
2(x + 3) = 3x - 1
2x + 6 = 3x - 1
3x - 2x = 6 + 1
x = 7
Put 7 for x in eq 1;
y = 7 + 3
y = 10
Thus, x = 7 and y = 10
