Section 15.3 Deliberate Practice: Solving by Substitution
Algebra is a skill, which means it requires practice to become proficient. But it will take more than rote repetition to get there. Deliberate practice is the thoughtful repetition of a task. For each of these sections, you will be given a list of specific skills or ideas to focus on as you practice thinking through the problems.
Focus on these skills:
Write the original system of equations.
Use sentences to organize the steps of your work, including a concluding statement.
Present your work legibly.
Worksheet Worksheet
Instructions: Determine the configuration of the system of equations. If they intersect at a single point, determine the coordinates of that point using the method of substitution.
1.
\(\left\{ \begin{array}{rcrcr} x \amp + \amp 2y \amp = \amp 7 \\ -2x \amp + \amp y \amp = \amp 1 \end{array} \right.\)
2.
\(\left\{ \begin{array}{rcrcr} x \amp - \amp 2y \amp = \amp 4 \\ -3x \amp + \amp 6y \amp = \amp -12 \end{array} \right.\)
3.
\(\left\{ \begin{array}{rcrcr} 3x \amp - \amp 2y \amp = \amp -8 \\ -x \amp + \amp 3y \amp = \amp 5 \end{array} \right.\)
4.
\(\left\{ \begin{array}{rcrcr} -2x \amp + \amp 3y \amp = \amp -8 \\ -x \amp + \amp 2y \amp = \amp -5 \end{array} \right.\)
5.
\(\left\{ \begin{array}{rcrcr} 2x \amp - \amp 3y \amp = \amp 1 \\ 4x \amp - \amp 6y \amp = \amp 4 \end{array} \right.\)
6.
\(\left\{ \begin{array}{rcrcr} 3x \amp + \amp 4y \amp = \amp 5 \\ 2x \amp + \amp 2y \amp = \amp 3 \end{array} \right.\)
7.
\(\left\{ \begin{array}{rcrcr} 2x \amp - \amp y \amp = \amp -4 \\ x \amp - \amp 2y \amp = \amp 5 \end{array} \right.\)
8.
\(\left\{ \begin{array}{rcrcr} -3x \amp - \amp 5y \amp = \amp -3 \\ x \amp + \amp y \amp = \amp 6 \end{array} \right.\)
9.
\(\left\{ \begin{array}{rcrcr} 3x \amp + \amp 3y \amp = \amp 4 \\ -3x \amp - \amp 2y \amp = \amp -1 \end{array} \right.\)
10.
\(\left\{ \begin{array}{rcrcr} 4x \amp + \amp 2y \amp = \amp -1 \\ 3x \amp + \amp 2y \amp = \amp 2 \end{array} \right.\)