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Solve the system using graphing, substitution or elimination. If needed round soulutions to the nearest tenth

Solve the system using graphing, substitution or elimination. If needed round soulutions-example-1
User Eske Rahn
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1 Answer

6 votes

Given

The system of equations,


\begin{gathered} 9x+y=45\text{ \_\_\_\_\_\lparen1\rparen} \\ x^3-3x^2-25x+93=y\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}

To find the solution.

Step-by-step explanation:

It is given that,


\begin{gathered} 9x+y=45\text{ \_\_\_\_\_\lparen1\rparen} \\ x^3-3x^2-25x+93=y\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}

From (1),


y=45-9x

Substitute y in (2).

Then,


\begin{gathered} x^3-3x^2-25x+93=45-9x \\ x^3-3x^2-25x+9x+93-45=0 \\ x^3-3x^2-16x+48=0 \\ x^2(x-3)-16(x-3)=0 \\ (x-3)(x^2-16)=0 \\ (x-3)(x^2-4^2)=0 \\ (x-3)(x-4)(x+4)=0 \end{gathered}

That implies,


\begin{gathered} x-3=0,x-4=0,x+4=0 \\ \text{ }x=3,\text{ }x=4,\text{ }x=-4 \end{gathered}

Therefore, for x=3,


\begin{gathered} y=45-9*3 \\ =45-27 \\ =18 \end{gathered}

For x=4,


\begin{gathered} y=45-9*4 \\ =45-36 \\ =9 \end{gathered}

For x=-4,


\begin{gathered} y=45-(9*-4) \\ =45+36 \\ =81 \end{gathered}

Hence, the solution set is (3,18), (4,9), (-4,81).

User Jfcogato
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