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What’s the correct answer

What’s the correct answer-example-1
User Matewilk
by
7.6k points

1 Answer

4 votes
Answer:

sundaes costs $
5.

banana splits costs $
6.

Explanation:

The matrix equation that represents the system is


\left[\begin{array}{cc}1&0\\5&4\\\end{array}\right] \left[\begin{array}{c}f\\b\\\end{array}\right] =\left[\begin{array}{c}5\\49\\\end{array}\right]

Method 1

Multiply the matrix equation to get,


1(f)+0(b)=5




5(f)+4(b)=49



\Rightarrow f=5

We do backward substitution to get,


25+4b=49


4b=49-25


4b=24


b=6



Method 2

The augmented matrix is


\left[\begin{array}{ccc}1&0&|5\\5&4&|49\end{array}\right]

We reduce to reduced row echelon form by performing the following row operations;


R_2-5R_1\rightarrow R_2.


\left[\begin{array}{ccc}1&0&|5\\0&4&|24\end{array}\right]

The next row operation is
(1)/(4) R_2\rightarrow R_2


\left[\begin{array}{ccc}1&0&|5\\0&1&|6\end{array}\right]

This implies that,


f=5 and
b=6

The correct answer is B
User Kennebec
by
8.4k points

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