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Can someone please explain how to get a and b step by step?

Can someone please explain how to get a and b step by step?-example-1
User Fstennet
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7.3k points

2 Answers

5 votes

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~~~

User Elias Prado
by
9.0k points
2 votes


3a-2b=13\\4a+b=21|\cdot2\\\\3a-2b=13\\\underline{8a+2b=42}\\11a=55\\a=5\\\\3\cdot5-2b=13\\2b=2\\b=1

User Mestachs
by
8.4k points

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