The solution to given equations by linear combination is (2, 3)
Solution:
Given equations are:
3x + 2y = 12 ----- eqn 1
y = 2x - 1
2x - y = 1 ------ eqn 2
Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated.
Addition is used when the two equations have terms that are exact opposites, and subtraction is used when the two equations have terms that are the same.
Let us solve eqn 1 and eqn 2 to find values of "x" and "y"
Multiply eqn 2 by 2
4x - 2y = 2 --- eqn 3
Add eqn 1 and eqn 3
3x + 2y = 12
4x - 2y = 2
(+) ------------------
7x = 14
x = 2
Substitute x = 2 in eqn 1
3x + 2y = 12
3(2) + 2y = 12
6 + 2y = 12
2y = 6
y = 3
Thus the solution to given equations is (2, 3)