Solving systems of linear equations in three variables unit 1 day 11

A-REI. 6: I can solve systems of linear equations exactly. A-REI A-REI.6: I can solve systems of linear equations exactly. A-REI.11: I know the point of intersection of multiple graphs is the solution to the equations. I can find the intersection point of a function using various methods.

Graphing in three dimensions three-dimensional coordinate plane ordered triple (x,y,z) eight octants z-axis plotting ordered triplets

Graphing in three dimensions Take Notes While Watching the Videos Watch this entire video (6 min) https://www.youtube.com/watch?v=VA5AmjhTA3A Watch only a portion of this video (1:15 – 5:05) https://www.youtube.com/watch?v=h5bOj9ztalI

Graphing in three dimensions Graph the following ordered triplets in your notes. Label each point. A (3, -2, 5) B (-4, 0, 1) C (2, 3, -7)

Decide whether the given ordered triple is a solution to the system.

Decide whether the given ordered triple is a solution to the system.

Number of solutions of a linear system The relationship between the graph of a linear system and the system’s number of solutions is illustrated below. If the planes intersect in a line, the system has infinitely many solutions. If the planes intersection in a single point, the system has exactly one solution (ordered triple). If the plane has no point of intersection, the system has no solution.

Using the Elimination Method to Solve the Linear System Watch each video intently. Do not take notes while watching the videos. Example of One Solution (watch the entirety of this video) https://www.youtube.com/watch?v=MJE4EPbQMD0 Example of One Solution (watch the entirety of this video) https://www.youtube.com/watch?v=JZDQRJVxw30 Example of Infinitely Many Solutions (only watch this video from the beginning through 3:15) https://www.youtube.com/watch?v=sG5LtfdpPDs Example of No Solution (watch the entirety of this video) https://www.khanacademy.org/math/algebra-home/alg-system-of-equations/alg-systems-with-three-variables/v/solutions-to-three-variable-system-2

GUIDED PRACTICE Using the Elimination Method to Solve the Linear System U1A11 Example 1 STEP 3: Use the equation that was not chosen in Step 1 and pair it with one of the other original equations to eliminate the y variable STEP 1: Identify two equations and a variable to eliminate STEP 2: Eliminate one of the variables in two of the original equations New Equation 2 New Equation 1

STEP 4: Solve the NEW system of equations using New Equation 1 and New Equation 2 STEP 5: Substitute the value from Step 4 into the either New Equation 1 or New Equation 2 and solve for x. STEP 6: Substitute you’re the values from Step 4 and Step 5 into any of the three original equations and solve for y.

GUIDED PRACTICE Using the Elimination Method to Solve the Linear System U1A11 Example 2 STEP 3: Use the equation that was not chosen in Step 1 and pair it with one of the other original equations to eliminate the x variable STEP 1: Identify two equations and a variable to eliminate STEP 2: Eliminate one of the variables in two of the original equations New Equation 2 New Equation 1

STEP 4: Solve the NEW system of equations using New Equation 1 and New Equation 2 STEP 5: Substitute the value from Step 4 into the either New Equation 1 or New Equation 2 and solve for y. STEP 6: Substitute you’re the values from Step 4 and Step 5 into any of the three original equations and solve for x.

GUIDED PRACTICE Using the Elimination Method to Solve the Linear System U1A11 Example 3 STEP 3: Use the equation that was not chosen in Step 1 and pair it with one of the other original equations to eliminate the z variable STEP 1: Identify two equations and a variable to eliminate STEP 2: Eliminate one of the variables in two of the original equations New Equation 2 New Equation 1

STEP 4: Solve the NEW system of equations using New Equation 1 and New Equation 2 STEP 5: Substitute the value from Step 4 into the either New Equation 1 or New Equation 2 and solve for y. STEP 6: Substitute you’re the values from Step 4 and Step 5 into any of the three original equations and solve for z.

INDEPENDENT PRACTICE U1A11 Example 4 Using the Elimination Method to Solve the Linear System U1A11 Example 4

INDEPENDENT PRACTICE U1A11 Example 4 Using the Elimination Method to Solve the Linear System U1A11 Example 4

INDEPENDENT PRACTICE U1A11 Example 5 Using the Elimination Method to Solve the Linear System U1A11 Example 5

INDEPENDENT PRACTICE U1A11 Example 5 Using the Elimination Method to Solve the Linear System U1A11 Example 5

Using the Reduced Row Echelon Form to Solve the Linear System Take notes while watching the first video. (watch the entirety of this video) https://www.youtube.com/watch?v=YwpoUPd6j-Y Grab your calculator and follow along with the instructor. (only watch this video from the beginning through 2:35) https://www.youtube.com/watch?v=e8mDRCIRbJU

INDEPENDENT PRACTICE Using the Reduced Row Echelon Form U1A11 Example 6 to Solve the Linear System

INDEPENDENT PRACTICE Using the Reduced Row Echelon Form U1A11 Example 6 to Solve the Linear System

INDEPENDENT PRACTICE Using the Reduced Row Echelon Form U1A11 Example 7 to Solve the Linear System

INDEPENDENT PRACTICE Using the Reduced Row Echelon Form U1A11 Example 7 to Solve the Linear System