ABCD is a parallelogram. If AB = 2x - y, CD = 7, BC = x + y , AD = 2 find x and y.
x+y = 2
2x-y = 7
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3 x = 9
x = 3
y = -1
impossible, typo ?
X=2X-3OR 2X-X=3;X=3 IF X=3 Ab=3 and BC=2×3-3=3
To find the values of x and y in the parallelogram ABCD, we can use the properties of a parallelogram.
In a parallelogram, opposite sides are equal in length. So we have the following equations:
AB = CD (opposite sides are equal) (1)
2x - y = 7 (substituting the given values)
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BC = AD (opposite sides are equal) (2)
x + y = 2 (substituting the given values)
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Now we have a system of two equations with two variables. We can solve them using substitution or elimination method.
From equation (2), we can write:
x = 2 - y
Substituting x = 2 - y into equation (1), we have:
2(2 - y) - y = 7
Simplifying the equation, we get:
4 - 2y - y = 7
4 - 3y = 7
-3y = 3
y = -1
Substituting the value of y into equation (2), we have:
x + (-1) = 2
x - 1 = 2
x = 3
Therefore, the values of x and y are x = 3 and y = -1, respectively.
To find the values of x and y, we can use the properties of a parallelogram.
In a parallelogram, opposite sides are equal in length. This means that AB = CD and AD = BC.
Given that AB = 2x - y, CD = 7, BC = x + y, and AD = 2, we can set up the following equations:
2x - y = 7 -- Equation 1
2 = x + y -- Equation 2
We now have a system of two equations that we can solve simultaneously.
To solve this system, we can use the method of substitution. We rearrange Equation 2 to solve for x as follows:
x = 2 - y
Now substitute this value of x into Equation 1:
2(2 - y) - y = 7
4 - 2y - y = 7
4 - 3y = 7
-3y = 7 - 4
-3y = 3
y = -1
Now substitute the value of y back into Equation 2 to find x:
x = 2 - (-1)
x = 2 + 1
x = 3
Therefore, the values of x and y are x = 3 and y = -1, respectively.