Solving 3-Variable Systems Using Elimination

1. Use the 3-variable system of equations below to answer the following questions.Equation 1: 4x + 4y + z = 24Equation 2: 2x - 4y + z = 0Equation 3: 5x - 4y - 5z = 12Which equationsand variables should you use to eliminate? *Remember you will have to add two equations on top of each other to eliminate. You can only eliminate variables that show the same number and opposite signs.* 1 2, eliminate the x's 1 2 eliminate the y's 1 3, eliminate the z's 2. What equation will you have after you effectively eliminate using your answer from the question above? 6x + 2z = 24 7x -4z = 12 6x -8y = 24 3. Now that you have one equation effectively eliminated to have be left with 2 variables. What are the next two equations you will have to use to eliminate?Equation 1: 4x + 4y + z = 24Equation 2: 2x - 4y + z = 0Equation 3: 5x - 4y - 5z = 12 1 2, eliminate the x's 1 3, eliminate the y's 2 3, eliminate the z's 4. You should now have two equations left. What will be your new 2-variable equations be? 5x + z = 20 8x - 3z = 32 -8y + 4z = 12 4y - 5z = 18 6x + 2z = 24 9x - 4z = 36 5. Now you will have to Manipulate one of the equations. Which equation will you have to manipulate and how? 2 [6x + 2z = 24] -2 [6x + 2z = 24] 2 [9x - 4z = 36] 6. Using your answer above, what will be the new equation after you have successfully manipulated? -12x - 2z = -48 12x + 4z = 48 18x - 8z = 72 7. After you successfully manipulate and then solve the 2-variable systems of equations, what will you be left with? x = -4 z = 4 x = 4 z = -4 8. Now plug inyour answer from the question above into one of the original 2-variable equations from question #4 to solve for the other variable.What will you have left after you complete this step? z = 0 x = 0 z = -4 x = -4 9. You're almost there! Now you will have to plug in the values of the two variables that you found into one of the original equations from question # 1. What will you have left after you plug in and solve? y = -2 y = 2 x = 2 x = -2 10. Which answer choice correctly shows the solutions to the 3-variable system of equations? (4, 2, 0) (-4, -2, 0) (4, -2, 0) (-4, 2, 0)