Answer:
- x +2y -1 = 3, x -4y +6 = 7
- x = 3, y = 1/2
Explanation:
(a)
The left side and the right side of the kite are equal lengths, so each is half the perimeter. That means AB = AD = 3, since half the perimeter is 10, and CB = CD = 7.
The two equations can be ...
AB = 3
x +2y -1 = 3
CB = 7
x -4y +6 = 7
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(b)
Subtracting the second from the first gives ...
(x +2y -1) -(x -4y +6) = (3) -(7)
6y -7 = 3 -7 . . . . simplify
6y = 3 . . . . . . . . add 7
y = 3/6 = 1/2 . . . . divide by 6
x +2(1/2) -1 = 3 . . . . substitute for y in the first equation
x = 3 . . . . . . . . simplify
The values of x and y are 3 and 1/2, respectively.
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Additional comment
We could collect the constants in the equations so they were all on the same side of the equal sign. As we saw above, that is not necessary.