Q33. Question If a+b=16,a-c=4,and聽b-... [FREE SOLUTION]

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Chapter 3: Q33. (page 144)

Question If $a + b = 16, a - c = 4, a n d b - c = - 4$ , which statement is true?
$\begin{matrix} 螜 . b + c = 12 \\ 螜螜 . a 鈭� b = 8 \\ 螜螜螜 . a + c = 20 \end{matrix}$
$(A) 螜$ only
$(B) 螜螜$ only
$(C) 螜 and 螜螜$ only
$(D) 螜, 螜螜, and 螜螜螜$

Short Answer

Expert verified

The option $(D)$ is true, the other options are false, because all the three equations $螜, 螜螜, 螜螜螜$ are true.

Step by step solution

– Use the elimination method to get the system of equations in two variables.

Subtract $a - c = 4$ from $a + b = 16$ as follows:

$\begin{array}{l} \underline{\begin{array}{l} 鈥夆赌夆赌夆赌夆赌� a + b 鈥夆赌夆赌夆赌� = 16 \\ (鈭�) a 鈥夆赌夆赌夆赌夆赌� 鈭� c = 鈥夆赌� 4 \end{array}} \\ 鈥夆赌夆赌夆赌夆赌� 0 + b + c = 12 \end{array}$

So, the resultant equation is $b + c = 12$ .

Subtract $b - c = - 4$ from $a + b = 16$ as follows:

$\begin{array}{l} \underline{\begin{array}{l} 鈥夆赌夆赌夆赌夆赌� a + b 鈥夆赌夆赌夆赌夆赌� = 鈥夆赌夆€� 16 \\ (鈭�) 鈥夆赌夆€� + b 鈭� c = 鈭� 鈥夆赌� 4 \end{array}} \\ 鈥夆赌夆赌夆赌夆赌� a + 0 + c = 鈥夆赌夆€� 20 \end{array}$

So, the resultant equation is $a + c = 20$ .

Subtract $b - c = - 4$ from $a - c = 4$ as follows

$\begin{array}{l} \underline{\begin{array}{l} 鈥夆赌夆赌夆赌夆赌� a 鈥夆赌夆赌夆赌夆赌� 鈭� c = 鈥夆赌夆€� 4 \\ (鈭�) 鈥夆赌夆€� + b 鈭� c = 鈭� 4 \end{array}} \\ 鈥夆赌夆赌夆赌夆赌� a 鈭� b + 0 = 鈥� 8 \end{array}$

So, the resultant equation is $a - b = 8$ .

– Check whether the option is true or false.

The given three equations are $螜 . b + c = 12, 螜螜 . a - b = 8, 螜螜螜 . a + c = 20$ .

From the above calculations in step 1, by using the equations $a + b = 16, a - c = 4,$ and $b - c = - 4$ , one can determine the all the given three equations $螜, 螜螜, 螜螜螜 .$

Here, in the option $(A)$ it is given that, $螜$ only.

But, all the three equations $螜, 螜螜, 螜螜螜$ can be determined.

So, option $(A)$ is false.

– Check whether the option B is true or false.

Here, in the option $(B)$ it is given that, $螜螜$ only.

But, all the three equations $螜, 螜螜, 螜螜螜$ can be determined.

So, option $(B)$ is false.

– Check whether the option C is true or false.

Here, in the option $(C)$ it is given that, $螜 and 螜螜$ only.

But, all the three equations $螜, 螜螜, 螜螜螜$ can be determined.

So, option $(C)$ is false.

– Check whether the option D is true or false.

Here, in the option $(D)$ it is given that, $螜, 螜螜, and 螜螜螜$ .

But, all the three equations $螜, 螜螜, 螜螜螜$ can be determined.

So, option $(D)$ is true.

Hence, the option $(D)$ is true, the other options are false, because all the three equations $螜, 螜螜, 螜螜螜$ are true.

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Question If $a + b = 16, a - c = 4, a n d b - c = - 4$ , which statement is true?
$\begin{matrix} 螜 . b + c = 12 \\ 螜螜 . a 鈭� b = 8 \\ 螜螜螜 . a + c = 20 \end{matrix}$
$(A) 螜$ only
$(B) 螜螜$ only
$(C) 螜 and 螜螜$ only
$(D) 螜, 螜螜, and 螜螜螜$

Short Answer

Step by step solution

– Use the elimination method to get the system of equations in two variables.

– Check whether the option is true or false.

– Check whether the option B is true or false.

– Check whether the option C is true or false.

– Check whether the option D is true or false.

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Question If a+b=16,a-c=4,andb-c=-4, which statement is true?螜.b+c=12螜螜.a鈭�b=8螜螜螜.a+c=20(A)螜only(B)螜螜only(C)螜and螜螜only(D)螜,螜螜,and螜螜螜

Short Answer

Step by step solution

– Use the elimination method to get the system of equations in two variables.

– Check whether the option is true or false.

– Check whether the option B is true or false.

– Check whether the option C is true or false.

– Check whether the option D is true or false.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Geometry

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Question If $a + b = 16, a - c = 4, a n d b - c = - 4$ , which statement is true?
$\begin{matrix} 螜 . b + c = 12 \\ 螜螜 . a 鈭� b = 8 \\ 螜螜螜 . a + c = 20 \end{matrix}$
$(A) 螜$ only
$(B) 螜螜$ only
$(C) 螜 and 螜螜$ only
$(D) 螜, 螜螜, and 螜螜螜$