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raketka [301]
2 years ago
13

Use the matrix tool to solve the system of equations. Choose the correct ordered pair.3x + 5y = 42 6x + 5y = 54

Mathematics
1 answer:
kobusy [5.1K]2 years ago
5 0
Solutions  

In Matrix we use initially based on systems of linear equations.The matrix method is similar to the method of Elimination as but is a lot cleaner than the elimination method.Solving systems of equations by Matrix Method involves expressing the system of equations in form of a matrix and then reducing that matrix into what is known as Row Echelon Form.<span> 

Calculations 

</span>⇒ <span>Rewrite the linear equations above as a matrix 
</span>
\left[\begin{array}{ccc}3&5&42\\6&5&54\\\end{array}\right] 

⇒  Apply to Row₂ : Row₂ - 2 <span>Row₁ 
</span>
\left[\begin{array}{ccc}3&5&42\\0&-5&-30\\\end{array}\right] 

⇒ <span>Simplify rows
</span>
\left[\begin{array}{ccc}3&5&42\\0&1&6\\\end{array}\right] 

Note: The matrix is now in echelon form.
<span>The steps below are for back substitution. 
</span>
⇒ Apply to Row₁<span> : Row</span>₁<span> - </span>5 Row₂ 

\left[\begin{array}{ccc}3&0&12\\0&1&6\\\end{array}\right] 

⇒ <span>Simplify rows 
</span>
\left[\begin{array}{ccc}1&0&4\\0&1&6\\\end{array}\right] 

⇒ <span>Therefore, 
</span>
x=4&#10;&#10;y = 6
<span> 

 
</span>

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<em><u>The system of equations that represents this situation are:</u></em>

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