Activity1.1.1

With a small number of unknowns, we are able to graph the sets of solutions to linear equations. Here, we will consider collections of equations having two unknowns.

  1. On the plot below, graph the lines

    \begin{equation*} \begin{split} y \amp = x+1 \\ y \amp = 2x-1 \\ \end{split} \text{.} \end{equation*}

    At what point or points \((x,y)\text{,}\) do the lines intersect? How many points \((x,y)\) satisfy both equations?

    <<SVG image is unavailable, or your browser cannot render it>>

  2. On the plot below, graph the lines

    \begin{equation*} \begin{split} y \amp = x+1 \\ y \amp = x-1. \\ \end{split} \end{equation*}

    At what point or points \((x,y)\text{,}\) do the lines intersect? How many points \((x,y)\) satisfy both equations?

    <<SVG image is unavailable, or your browser cannot render it>>

  3. On the plot below, graph the line

    \begin{equation*} y = x+1 \text{.} \end{equation*}

    How many points \((x,y)\) satisfy this equation?

    <<SVG image is unavailable, or your browser cannot render it>>

  4. On the plot below, graph the lines

    \begin{equation*} \begin{split} y \amp = x+1 \\ y \amp = 2x-1 \\ y \amp = -x. \\ \end{split} \end{equation*}

    At what point or points \((x,y)\text{,}\) do the lines intersect? How many points \((x,y)\) satisfy all three equations?

    <<SVG image is unavailable, or your browser cannot render it>>

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