Mathematics: Asystem of equations is showny=3x-2 y=x^2what are the solutions to the systems of equations?

Asystem of equations is showny=3x-2 y=x^2what are

Ответ:

lalllda

12.03.2022

$\bf \begin{cases}
\boxed{y}=3x-2\\
y=x^2
\end{cases}~\hspace{6em}\stackrel{\textit{doing a quick substitution}}{\boxed{3x-2}=x^2}\implies 0=x^2-3x+2
\\\\\\
0=(x-1)(x-2)\implies
\begin{cases}
0=x-1\implies &1=x\\[0.8em]
0=x-2\implies &2=x
\end{cases}
\\\\[-0.35em]
~\dotfill$

$\bf \stackrel{\textit{using x = 1 in the first equation}}{y=3(1)-2\implies y=1}~\hfill \blacktriangleright (\stackrel{x}{1},\stackrel{y}{1}) \blacktriangleleft
\\\\\\
\stackrel{\textit{using x = 2 in the first equation}}{y=3(2)-2\implies y=4}~\hfill \blacktriangleright (\stackrel{x}{2},\stackrel{y}{4})\blacktriangleleft$

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Asystem of equations is showny=3x-2 y=x^2what are the solutions to the systems of equations?

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