ABCD is a parallelogram. Find x and y using the following information:
AB = 5x - 2y
DC = 4
AD = y
BC = 5 - x
In a ||gram , opposite sides are equal, so
5x-2y = 4 and 5-x = y
Solve as a pair of equations in two unknowns
(I would use substitution, subbing the second into the first)
To find x and y in the parallelogram ABCD, we can use the properties of parallelograms.
In a parallelogram, opposite sides are equal in length. So, we can set up equations using the given information:
AB = DC (Opposite sides of a parallelogram are equal in length)
5x - 2y = 4
AD = BC (Opposite sides of a parallelogram are equal in length)
y = 5 - x
Now, we have a system of two equations with two variables. We can solve this system by substituting the value of y from the second equation into the first equation:
5x - 2(5 - x) = 4
Simplify the equation:
5x - 10 + 2x = 4
7x - 10 = 4
Add 10 to both sides:
7x = 14
Divide both sides by 7:
x = 2
Now, substitute the value of x into the second equation to find y:
y = 5 - x
y = 5 - 2
y = 3
Therefore, x = 2 and y = 3.