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kudzordzifrancis
Answer:

sundaes costs $ [tex]5[/tex].

banana splits costs $ [tex]6[/tex].

Step-by-step explanation:

The matrix equation that represents the system is

[tex]\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][/tex]

Method 1

Multiply the matrix equation to get,

[tex]1(f)+0(b)=5[/tex]



[tex]5(f)+4(b)=49[/tex]


[tex]\Rightarrow f=5[/tex]

We do backward substitution to get,

[tex]25+4b=49[/tex]

[tex]4b=49-25[/tex]

[tex]4b=24[/tex]

[tex]b=6[/tex]



Method 2

The augmented matrix is

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

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

[tex]R_2-5R_1\rightarrow R_2[/tex].

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

The next row operation is [tex]\frac{1}{4} R_2\rightarrow R_2[/tex]

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

This implies that,

[tex]f=5[/tex] and [tex]b=6[/tex]

The correct answer is B

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