example 1 solution by elimination chapter 7.1 solve the system 2009 pblpathways
TRANSCRIPT
example 1 Solution by Elimination
Chapter 7.1
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
2009 PBLPathways
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
1. If necessary, interchange two equations or use multiplication to make the coefficient of x in the first equation a 1.
2 3
2 3 1
3 9
x y z
x y z
x y z
E1 E22 3 1
2 3
3 9
x y z
x y z
x y z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
2. Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become 0.
2 3
3 5
3 9
x y z
y z
x y z
2 3
2 3 1
3 9
x y z
x y z
x y z
-2 R1 + R2 R2
2 2 4 6
2 3 1
3 5
x y z
x y z
y z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
2. Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become 0.
2 3
3 5
3 9
x y z
y z
x y z
2 3
2 3 1
3 9
x y z
x y z
x y z
-2 E1 + E2 E2
2 2 4 6
2 3 1
3 5
x y z
x y z
y z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
2. Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become 0.
2 3
3 5
3 9
x y z
y z
x y z
2 3
2 3 1
3 9
x y z
x y z
x y z
-2 E1 + E2 E2
2 2 4 6
2 3 1
3 5
x y z
x y z
y z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
2. Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become 0.
-3 R1 + R3 R3
3 3 6 9
3 9
4 7 18
x y z
x y z
y z
2 3
3 5
3 9
x y z
y z
x y z
2 3
3 5
4 7 18
x y z
y z
y z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
2. Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become 0.
-3 E1 + E3 E3
3 3 6 9
3 9
4 7 18
x y z
x y z
y z
2 3
3 5
3 9
x y z
y z
x y z
2 3
3 5
4 7 18
x y z
y z
y z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
2. Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become 0.
-3 E1 + E3 E3
3 3 6 9
3 9
4 7 18
x y z
x y z
y z
2 3
3 5
3 9
x y z
y z
x y z
2 3
3 5
4 7 18
x y z
y z
y z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
2. Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become 0.
-3 E1 + E3 E3
3 3 6 9
3 9
4 7 18
x y z
x y z
y z
2 3
3 5
3 9
x y z
y z
x y z
2 3
3 5
4 7 18
x y z
y z
y z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
3. Multiply (or divide) both sides of the second equation by a number that makes the coefficient of y in the second equation equal to 1.
2 3
3 5
4 7 18
x y z
y z
y z
2 3
3 5
4 7 18
x y z
y z
y z
-1 R2 R2
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
3. Multiply (or divide) both sides of the second equation by a number that makes the coefficient of y in the second equation equal to 1.
2 3
3 5
4 7 18
x y z
y z
y z
2 3
3 5
4 7 18
x y z
y z
y z
-1 E2 E2
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
3. Multiply (or divide) both sides of the second equation by a number that makes the coefficient of y in the second equation equal to 1.
2 3
3 5
4 7 18
x y z
y z
y z
2 3
3 5
4 7 18
x y z
y z
y z
-1 E2 E2
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
4. Add a multiple of the (new) second equation to the (new) third equation so that the coefficient of y in the newest third equation becomes 0.
2 3
3 5
19 38
x y z
y z
z
2 3
3 5
4 7 18
x y z
y z
y z
-4 R2 + R3 R3
4 12 20
4 7 18
19 38
y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
4. Add a multiple of the (new) second equation to the (new) third equation so that the coefficient of y in the newest third equation becomes 0.
2 3
3 5
19 38
x y z
y z
z
2 3
3 5
4 7 18
x y z
y z
y z
-4 E2 + E3 E3
4 12 20
4 7 18
19 38
y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
4. Add a multiple of the (new) second equation to the (new) third equation so that the coefficient of y in the newest third equation becomes 0.
2 3
3 5
19 38
x y z
y z
z
2 3
3 5
4 7 18
x y z
y z
y z
-4 E2 + E3 E3
4 12 20
4 7 18
19 38
y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
4. Add a multiple of the (new) second equation to the (new) third equation so that the coefficient of y in the newest third equation becomes 0.
2 3
3 5
19 38
x y z
y z
z
2 3
3 5
4 7 18
x y z
y z
y z
-4 E2 + E3 E3
4 12 20
4 7 18
19 38
y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
5. Multiply (or divide) both sides of the third equation by a number that makes the coefficient of z in the third equation equal to 1. This gives the solution for z in the system of equations.
2 3
3 5
2
x y z
y z
z
2 3
3 5
19 38
x y z
y z
z
E3 E3119
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
5. Multiply (or divide) both sides of the third equation by a number that makes the coefficient of z in the third equation equal to 1. This gives the solution for z in the system of equations.
2 3
3 5
2
x y z
y z
z
2 3
3 5
19 38
x y z
y z
z
E3 E3119
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
6. Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.
3 2 5
6 5
1
y
y
y
1 2 2 3
5 3
2
x
x
x
2 3
3 5
2
x y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
6. Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.
3 2 5
6 5
1
y
y
y
1 2 2 3
5 3
2
x
x
x
2 3
3 5
2
x y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
6. Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.
3 2 5
6 5
1
y
y
y
1 2 2 3
5 3
2
x
x
x
2 3
3 5
2
x y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
6. Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.
3 2 5
6 5
1
y
y
y
1 2 2 3
5 3
2
x
x
x
2 3
3 5
2
x y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
6. Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.
3 2 5
6 5
1
y
y
y
1 2 2 3
5 3
2
x
x
x
2 3
3 5
2
x y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
6. Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.
3 2 5
6 5
1
y
y
y
1 2 2 3
5 3
2
x
x
x
2 3
3 5
2
x y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
6. Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.
3 2 5
6 5
1
y
y
y
1 2 2 3
5 3
2
x
x
x
2 3
3 5
2
x y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
6. Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.
3 2 5
6 5
1
y
y
y
1 2 2 3
5 3
2
x
x
x
2 3
3 5
2
x y z
y z
z
2009 PBLPathways
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
6. Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.
3 2 5
6 5
1
y
y
y
1 2 2 3
5 3
2
x
x
x
2 3
3 5
2
x y z
y z
z
2009 PBLPathways
Does the solution solve the system?
Solve the system2 3 1
2 3
3 9
x y z
x y z
x y z
2 2 3 1 2 1
2 1 2 2 3
3 2 1 2 9