Upcoming SlideShare
×

Alg2 lesson 3-5

417 views

Published on

Published in: Education, Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
417
On SlideShare
0
From Embeds
0
Number of Embeds
37
Actions
Shares
0
0
0
Likes
0
Embeds 0
No embeds

No notes for slide

Alg2 lesson 3-5

1. 1. First equation<br />Third equation<br />Subtract to eliminate z.<br />Notice that the z terms in each equation have been eliminated. The result istwo equations with the two same variables x and y.<br />Example 5-1a<br />
2. 2. Add to eliminate y.<br />Divide by 29.<br />Equation with two variables<br />Multiply by 5.<br />Replace x with –2.<br />Multiply.<br />Simplify.<br />Step 2Solve the system of two equations. <br />Substitute –2 for x in one of the two equations with two variables and solve for y.<br />Example 5-1a<br />
3. 3. Equation with three variables<br />Replace x with –2 and y with 6.<br />Multiply.<br />Simplify.<br />Step 3Substitute –2 for x and 6 for yin one of the original equations with three variables.<br />Answer: The solution is (–2, 6, –3). You can check this solution in the other two original equations.<br />Example 5-1a<br />
4. 4. Solve the system of equations.<br />Pick a variable to eliminate from all three equations.<br />Example 5-1b<br />
5. 5. Solve the system of equations.<br />Use two equations at a time to eliminate the same variable.<br />2x + 3y – 3z = 16<br />−2x – 2y – 2z = 6<br />2x + 3y – 3z = 16<br /> x + y + z = – 3<br />• – 2<br />y – 5z = 22<br />Example 5-1b<br />
6. 6. Solve the system of equations.<br />Use two other equations to eliminate the same variable.<br />2x + 3y – 3z = 16<br />−2x + 4y + 2z = 2<br />2x + 3y – 3z = 16<br /> x – 2y – z = – 1<br />• – 2<br />7y – z = 18<br />Example 5-1b<br />
7. 7. Solve the new system of equations.<br />y – 5z = 22<br />y – 5z = 22<br />• – 5<br />7y – z = 18<br />– 35y+5z = – 90<br />– 34y = – 68<br /> y = 2 <br />7(2) – z = 18<br />14 – z = 18<br />– z = 4<br />z = – 4<br />
8. 8. y = 2 <br />z = – 4<br />Solve for the remaining variable.<br />x + y + z = – 3<br />x + 2 + – 4 = – 3<br />x – 2 = – 3<br />x = – 1<br />Answer:(–1, 2, –4)<br />Example 5-1b<br />
9. 9. Answer:(–1, 2, –4)<br />Check!!!<br />2(– 1) + 3(2) – 3(–4) = 16<br />– 1 + 2 + –4 = – 3<br />– 1 – 2(2) – (–4) = – 1<br />Example 5-1b<br />
10. 10. Solve the system of equations.<br />Answer: The solution is (–2, 6, –3)..<br />Example 5-1a<br />
11. 11. Solve the system of equations.<br />Multiply by 3.<br />Multiply by 2.<br />Answer: The equation is never true. So, there is no solution of this system.<br />Eliminate x in the second two equations.<br />Example 5-3a<br />
12. 12. Solve the system of equations.<br />Multiply by 3.<br />Eliminate y in the first and third equations.<br />Example 5-2a<br />
13. 13. The equation is always true. This indicates that the first and third equations represent the same plane. Check to see if this plane intersects the second plane.<br />Divide by the GCF, 3.<br />Multiply by 6.<br />Answer: The planes intersect in a line. So, there are an infinite number of solutions.<br />Example 5-2a<br />
14. 14. Solve the system of equations.<br />Answer:There are an infinite number of solutions.<br />Example 5-2b<br />
15. 15. Solve the system of equations.<br />Answer:There is no solution of this system.<br />Example 5-3b<br />