Answer:
a = 5, b = 1
Explanation:
We need to realize that in a parallelogram, opposite sides are congruent. Therfore, the length of NO and MP must be the same if we assume that Quadrilateral MNOP is a parallelogram.
Length of NO = 21
Length of MP = 4a + b
Therfore, we can get this equation: 4a + b = 21
We can do the same with the other 2 sides to get: 3a - 2b = 13
As you can see, this is a systems of equations! Lets solve it!
To find the values of "a" and "b" in the given system of equations:
Equation 1: 4a + b = 21
Equation 2: 3a - 2b = 13
We can solve this system of equations using either the substitution method or the elimination method. Let's use the elimination method:
Multiply Equation 1 by 2:
2(4a + b) = 2(21)
8a + 2b = 42
Now, we can add Equation 2 and the modified Equation 1 to eliminate the "b" term:
(3a - 2b) + (8a + 2b) = 13 + 42
3a + 8a - 2b + 2b = 55
11a = 55
Divide both sides of the equation by 11:
a = 55 / 11
a = 5
Substitute the value of "a" into Equation 1 to find "b":
4(5) + b = 21
20 + b = 21
b = 21 - 20
b = 1
Therefore, the solution to the system of equations is a = 5 and b = 1.
Therfore, the answer is B, which is what you got as well! Good job!
~~~Harsha~~~