Question

What is Linear combination method? Explain with an example.

Answer 1

Linear combination is a method to solve a system algebraically. The goal of solving system is to reduce the system that has two equations in two variables to a single equation that has only one variable. In linear combination, the two equations are added together, resulting in an equation containing only one unknown and easily we can solve the system.......
example:-
7x - y = 5 and 2x + 3y = 8

Solution:
The given equations are
7X - y = 5 ..................(1)
2x + 3y = 8 ......................... (2)
Multiply by 3 to the equation (1)
21x - 3y = 15 .............................(3)
Multiply by 1 to the equation (2)
2x + 3y = 8 ............................. (4)
Add equation (3) and equation (4)
21x - 3y + (2x + 3y) = 15 + 8
21x - 3y + 2x + 3y = 15 + 8
Combine like terms.
21x + 2x - 3y + 3y = 23
23x = 23
Isolate the variable x.
x = 1
Substitute the value of x variable into the equation (2)
2x + 3y = 8
2(1) + 3y = 8
2 + 3y = 8
Subtract 2 from each side.
2 - 2 + 3y = 8 - 2
3y = 6
Isolate the variable y.
Y = 2
the solutions are x = 1 and y = 2.