Before I go on and give you the problenms let me explain. i am not some lazy kid trin to get people to do my homework over the internet. I am freshman that just recently skippeda garde in math and I need some help. The problems below are from my pop quiz out of the text book i gotta hand in on monday. I can't ahve my aad or mom checkin this cause they have no clue on this but i did the problems and need feed bac.
solve the system using linear combination method
12. 3x+ 2y-z=8
-3x+4y+5z=-14
x-3y+4z=-14
(my answer was (1,1,-3))
16. x+y-2z=5
x+2y+z=8
2x+3y-z=13
(my answer was infinite solution)
18. -2x+y+6z=1
3x+2y+5z=16
7x+3y-4z=11
(my answer was in fraction form but she said no solutions were fractions)
I appreciate your effort in attempting these problems on your own. Let's go through each problem and I'll explain how to solve them using the linear combination method.
12. To solve the system using the linear combination method, you'll want to eliminate one variable at a time. Start with the x variable. To eliminate x, add the first equation with the second equation. This will cancel out the x terms. Now, add the result to the third equation. This will eliminate the x variable from all three equations.
Once you've eliminated x, you'll be left with two equations involving only y and z. Solve these equations simultaneously to find the values of y and z. Then substitute these values back into any of the original equations to find the value of x.
16. Again, start by eliminating one variable at a time. This time, let's eliminate the z variable. Add the first equation with twice the second equation. This will cancel out the z terms. Now, add the result to three times the third equation. This will eliminate the z variable from all three equations.
Once you've eliminated z, you'll be left with two equations involving only x and y. Solve these equations simultaneously to find the values of x and y. Since you have an infinite solution, you'll find that x and y can take on any value. However, the value of z is not determined in this case.
18. Similar to the previous problems, start by eliminating one variable at a time. Let's eliminate the x variable this time. Multiply the first equation by 3 and the second equation by 2. Then, add the two equations to eliminate x. Now, add the result to seven times the third equation. This will eliminate the x variable from all three equations.
Once you've eliminated x, you'll be left with two equations involving only y and z. Solve these equations simultaneously to find the values of y and z. It's important to note that your answer should be in fraction form if that's what the calculations yield. If you didn't get a fraction, please check your calculations again to ensure accuracy.
Remember, double-checking your calculations and ensuring that you accurately eliminate the variables in each step is crucial for getting the correct solution. Don't hesitate to seek further clarification or assistance if needed. Good luck with your assignment!