Introduction on long math problem
This article is about long math problem. Long math problem will contain a lot of step in solving the problem to obtain the final solution. In some of the long math problem we use different formula to obtain the solution. There are many long math problem in many different math chapters. Each topics of mathematics have different solving properties theorem methods and formulas. There are many websites and online tutors to help with long math problem. Many stiudents favorite and best website to solve long math problem is tutor vista. Below we can see one long math problem.
Long Math Problem
Long math problem does not means that the given problem must be long. It also means the steps taken to solve some problems lead to long math problem. Below we solved one math problem which have a long steps to obtain the entire solution.
1. Solve the equations: p + 2q + 3r = 14, 3p + q + 2r = 11, 2p + 3q + r = 11.
Solution: Let the given equations be identified as follows:
p + 2q + 3r = 14------- (1)
3p + q + 2r = 11------ (2)
2p + 3q + r = 11------ (3)
Consider the equations (1) and (3)
(1) ? p + 2q + 3r = 14
(3) × 3 ? 6p + 9q + 3r = 33 subtracting
–5p – 7q = –19
5p + 7q = 19 (4)
Consider the equations (2) and (3)
(2) ? 3p + q + 2r = 11
(3) × 2 ? 4p + 6q + 2r = 22 subtracting
–p – 5q = –11
p + 5q = 11 (5)
Consider the equations (4) and (5)
(4) ? 5p + 7q = 19
(5) × 5 ? 5p + 25q = 55 subtracting
–18q = –36; ?q = 2
Substitute q = 2 in (5) we get
p + 5(2) = 11; p + 10 = 11; ?p= 1
Substitute p = 1, q = 2 in (3) we get
2(1) + 3(2) + r = 11; 2 + 6 + r = 11 ? r = 3
The solution is p = 1, q = 2, r = 3.
Long Math Problem
Similar to the above problem there are more number of math problems to solve with long steps. In some problems the given math problem will be long and the solution will be a shorter one. In some cases the solution and the problem both will be a longer one. Here are some problem similar to the solved problem above for your practice. The solution also given below and you have to try the steps similar to the problem solved above.
1. Solve: 3x – 3y + 4z = 14; –9x – 6y + 2z = 1; 6x + 3y + z = 5
Answer: The solution is x = 1, y = –1, z = 2
2. Solve: a + b = 3, b + c = –5, c + a = 2.
Answer: The solution is a = 5, b = –2, c = –3.
This article is about long math problem. Long math problem will contain a lot of step in solving the problem to obtain the final solution. In some of the long math problem we use different formula to obtain the solution. There are many long math problem in many different math chapters. Each topics of mathematics have different solving properties theorem methods and formulas. There are many websites and online tutors to help with long math problem. Many stiudents favorite and best website to solve long math problem is tutor vista. Below we can see one long math problem.
Long Math Problem
Long math problem does not means that the given problem must be long. It also means the steps taken to solve some problems lead to long math problem. Below we solved one math problem which have a long steps to obtain the entire solution.
1. Solve the equations: p + 2q + 3r = 14, 3p + q + 2r = 11, 2p + 3q + r = 11.
Solution: Let the given equations be identified as follows:
p + 2q + 3r = 14------- (1)
3p + q + 2r = 11------ (2)
2p + 3q + r = 11------ (3)
Consider the equations (1) and (3)
(1) ? p + 2q + 3r = 14
(3) × 3 ? 6p + 9q + 3r = 33 subtracting
–5p – 7q = –19
5p + 7q = 19 (4)
Consider the equations (2) and (3)
(2) ? 3p + q + 2r = 11
(3) × 2 ? 4p + 6q + 2r = 22 subtracting
–p – 5q = –11
p + 5q = 11 (5)
Consider the equations (4) and (5)
(4) ? 5p + 7q = 19
(5) × 5 ? 5p + 25q = 55 subtracting
–18q = –36; ?q = 2
Substitute q = 2 in (5) we get
p + 5(2) = 11; p + 10 = 11; ?p= 1
Substitute p = 1, q = 2 in (3) we get
2(1) + 3(2) + r = 11; 2 + 6 + r = 11 ? r = 3
The solution is p = 1, q = 2, r = 3.
Long Math Problem
Similar to the above problem there are more number of math problems to solve with long steps. In some problems the given math problem will be long and the solution will be a shorter one. In some cases the solution and the problem both will be a longer one. Here are some problem similar to the solved problem above for your practice. The solution also given below and you have to try the steps similar to the problem solved above.
1. Solve: 3x – 3y + 4z = 14; –9x – 6y + 2z = 1; 6x + 3y + z = 5
Answer: The solution is x = 1, y = –1, z = 2
2. Solve: a + b = 3, b + c = –5, c + a = 2.
Answer: The solution is a = 5, b = –2, c = –3.
