SOLVING SYSTEMS OF LINEAR EQUATIONS IN THREE VARIABLES

SOLVING SYSTEMS OF LINEAR EQUATIONS IN THREE VARIABLES UNIT 1

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=VA 5 Amjh. T A 3 A Watch only a portion of this video (1: 15 – 5: 05) https: //www. youtube. com/watch? v=h 5 b. Oj 9 ztal. I

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.

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. (watch the entirety of this video) Example of One Solution https: //www. youtube. com/watch? v=MJE 4 EPb. QMD 0 (watch the entirety of this video) Example of One Solution https: //www. youtube. com/watch? v=JZDQRJVxw 30 (only watch this video from the beginning through 3: 15) Example of Infinitely Many Solutions https: //www. youtube. com/watch? v=s. G 5 Ltfdp. PDs (watch the entirety of this video) Example of No Solution https: //www. khanacademy. org/math/algebra-home/alg-system-of-equations/alg-systems-withthree-variables/v/solutions-to-three-variable-system-2

Writing Utensil Down

GUIDED PRACTICE Using the Elimination Method to Solve the Linear System Example 1 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 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 New Equation 2

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.

Thinking Map: Sequence of Steps

GUIDED PRACTICE Using the Elimination Method to Solve the Linear System Example 2 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 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 x variable New Equation 2

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.

Thinking Map: Sequence of Steps/Written Explanation

GUIDED PRACTICE Using the Elimination Method to Solve the Linear System Example 3 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 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 z variable New Equation 2

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.

Thinking Map: Sequence of Steps/Written Explanation

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

INDEPENDENT PRACTICE Using the Elimination Method to Solve the Linear System 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=Ywpo. UPd 6 j-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=e 8 m. DRCIRb. JU

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

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