Section 15.2 Worksheets
PDF Version of these Worksheets
Worksheet Worksheet 1
1.
Graph the lines and describe their configuration.
2.
Graph the lines and describe their configuration.
3.
Determine whether is a solution of the system of equations.
\begin{equation*}
\left\{ \begin{array} {rcrcr}
2x \amp + \amp y \amp = \amp -5 \\
x \amp - \amp 3y \amp = \amp -1
\end{array} \right.
\end{equation*}
Worksheet Worksheet 2
1.
Describe the configuration of the following system of equations. If they intersect at a single point, determine the coordinates of that point.
\begin{equation*}
\left\{ \begin{array} {rl}
y \amp = 3 x + 3 \\
y \amp = 2 x - 1
\end{array} \right.
\end{equation*}
2.
Describe the configuration of the following system of equations. If they intersect at a single point, determine the coordinates of that point.
\begin{equation*}
\left\{ \begin{array} {rl}
y \amp = -2x + 5 \\
y \amp = x - 1
\end{array} \right.
\end{equation*}
3.
Describe the configuration of the following system of equations. If they intersect at a single point, determine the coordinates of that point.
\begin{equation*}
\left\{ \begin{array} {rl}
y \amp = 3x + 1 \\
y \amp = -x - 2
\end{array} \right.
\end{equation*}
Worksheet Worksheet 3
1.
Describe the configuration of the following system of equations. If they intersect at a single point, determine the coordinates of that point.
\begin{equation*}
\left\{ \begin{array} {rcrcr}
x \amp + \amp y \amp = \amp 6 \\
x \amp - \amp y \amp = \amp 2
\end{array} \right.
\end{equation*}
2.
Describe the configuration of the following system of equations. If they intersect at a single point, determine the coordinates of that point.
\begin{equation*}
\left\{ \begin{array} {rcrcr}
3x \amp - \amp 2y \amp = \amp 4 \\
-6x \amp + \amp 4y \amp = \amp -8
\end{array} \right.
\end{equation*}
3.
Describe the configuration of the following system of equations. If they intersect at a single point, determine the coordinates of that point.
\begin{equation*}
\left\{ \begin{array} {rcrcr}
2x \amp + \amp y \amp = \amp 3 \\
4x \amp + \amp 2y \amp = \amp -3
\end{array} \right.
\end{equation*}
Worksheet Worksheet 4
1.
Describe the configuration of the following system of equations. If they intersect at a single point, determine the coordinates of that point.
\begin{equation*}
\left\{ \begin{array} {rcrcr}
2x \amp - \amp y \amp = \amp 7 \\
-x \amp + \amp 3y \amp = \amp -1
\end{array} \right.
\end{equation*}
2.
Describe the configuration of the following system of equations. If they intersect at a single point, determine the coordinates of that point.
\begin{equation*}
\left\{ \begin{array} {rcrcr}
x \amp + \amp 3y \amp = \amp 0 \\
2x \amp + \amp 5y \amp = \amp -1
\end{array} \right.
\end{equation*}
3.
Describe the configuration of the following system of equations. If they intersect at a single point, determine the coordinates of that point.
\begin{equation*}
\left\{ \begin{array} {rcrcr}
3x \amp - \amp 4y \amp = \amp -6 \\
-4x \amp + \amp 2y \amp = \amp -5
\end{array} \right.
\end{equation*}
Worksheet Worksheet 5
1.
Suppose that \(m_1 \neq m_2\text{.}\) Then the following system of equations intersect at a single point. Determine the coordinates of that point.
\begin{equation*}
\left\{ \begin{array} {rl}
y \amp = m_1 x + b_1 \\
y \amp = m_2 x + b_2
\end{array} \right.
\end{equation*}
2.
Suppose that the following system of equations intersect at a single point. Determine the coordinates of that point.
\begin{equation*}
\left\{ \begin{array} {rcrcr}
ax \amp + \amp by \amp = \amp c \\
dx \amp + \amp ey \amp = \amp f
\end{array} \right.
\end{equation*}
