ABCD is a parallelogram. BM= 22-3x, DM=10+9x, AM=7y+13 and CM=2y+38. solve for x and y
Where is M?
I can only assume M is the intersection of the diagonals, since there seems to be a line from each vertex to M.
In a parallelogram, the diagonals bisect each other. That means, assuming that ABCD are the vertices labeled in order,
AM=CM and BM=DM
7y+13 = 2y+38
5y = 25
y=5
22-3x = 10+9x
12x = 12
x=1
Looking at all my assumptions, maybe you can see why it is important to explain fully any diagrams you intend to use...
To solve for x and y in the given parallelogram ABCD, we will use the properties of parallelograms.
In a parallelogram, opposite sides are equal in length. So, we can set up the following equations:
BM = DM (opposite sides)
22 - 3x = 10 + 9x
AM = CM (opposite sides)
7y + 13 = 2y + 38
Let's solve each equation separately:
1) Solving for x:
22 - 3x = 10 + 9x
Rearrange the equation to isolate x terms on one side:
22 - 10 = 9x + 3x
12 = 12x
Divide both sides by 12:
x = 1
So, we have found the value for x, which is x = 1.
2) Solving for y:
7y + 13 = 2y + 38
Rearrange the equation to isolate y terms on one side:
7y - 2y = 38 - 13
5y = 25
Divide both sides by 5:
y = 5
So, we have found the value for y, which is y = 5.
Therefore, the solutions for x and y in the given parallelogram ABCD are x = 1 and y = 5.