 |
|
| Browse | Ask | Answer | Search | Join/Login |
|
|
||||
|
Algebra II Help Systems of Equations..
Homework Help, Can you help me by explain what to do to get to the answer, I am stumped because there's only on x variable, so there's not a way to eliminate or substitute, IS THERE?
What does x equal in the solution of the system of equations below? x + 2y + z = 4 4y – 3z = 1 2y + 10z = 12 |
||||
|
|
|
||||
|
x=12.3 or 12 1/3 |
||||
|
|
|
||||
|
You take the second and third equations and try to solve them simultaneously. Using the values of y and z you got there, you use that in the first equation to find the value of x in the first equation. This is the procedure. If all three equations have 3 variables, then, you would have to make one variable the subject of formula so that you can get one equation with two variables from two equations (or another way so that you can make two equations with only two variables from 3 equations with 3 variables). This is a little difficult to understand, I know, but if you want an example, I can post one. |
||||
|
|
|
||||
|
Yeah, an example would be great! :] |
||||
|
|
|
||||
|
Ok, let's say: x + 2y + 3z = 5 2x + y + z = 3 x + 2y + 5z = 9 (just using random numbers, so the results may not be 'pretty numbers'. From there, you have 3 equations, 3 variables. Take 1 and 2: x + 2y + 3z = 5... a 2x + y + z = 3 : x2 -> 4x + 2y + 2z = 6... b Subtract a from b: 4x - x + 2y - 2y + 2z - 3z = 6-5 3x - z = 1... I From 2 and 3: 2x + y + z = 3 : x2 --> 4x + 2y + 2z = 6... c x + 2y + 5z = 9... d Subtract d from c: 4x - x +2y - 2y +2z- 5z = 6 - 9 3x - 3z = -3... II From I and II, solve simultaneously, by subtracting II from I: 3x - 3x -3z -(-z) = -3 - 1 -2z = -4 z = 2 Now, use that z in equation I or II to get x. 3x - (2) = 1 x = 1 or 3x - 3z = -3 x - z = -1 x - (2) = -1 x = 1 From the values of x and z, you can find y: (1) + 2y + 3(2) = 5 : y = -1 2(1) + y + (2) = 3 : y = -1 (1) + 2y + 5(2) = 9 : y = -1 You see? However, surprisingly, I got whole numbers, which isn't always the case when you take random numbers like that. |
||||
|
|
|
||||
|
You could also use matrices. Just involve a 0 variable for the missing link. Ax + by + cz = f Where x is missing a = 0. |
||||
|
|
| Question Tools | Search this Question |
Check out some similar questions!
As a business owner there are many decisions that you need to make on a daily basis, such as ensuring you reach the highest production levels possible with your company’s products. Your company produces two models of bicycles: Model A and Model B. Model A takes 2 hours to assemble, where Model B...
Can someone help me with this problem? I'd be grateful. The Everton College store paid 1532 for an order of 42 calculators. The store paid $8 ea. for science calculators. The others, all graphing calculators, cost the store $54 ea. How many of each type of calculators was ordered? Thank-you for...
How do you solve systems of equations with 3 variables? And what if one of the equations only has 2 of the variables? Example: 1) 2x+3y-4z=20 2) 3x-2y+z=12 3) 5x-2z=4 Don't try to solve this one, I just made it up to give you an example.
1. x + 2y = 7 3x - 2y = -3
Ok I have been trying to figure these 3 problems out and I know its probably something very simple as I can do other problems like them that are similar but these are racking my brain please help! 1. Write a system of equation where the solution is (-2,1) 2. This I need to find out x and y...
View more questions Search
|
