Final answer:
To solve the system of equations using the linear combination method, we multiply the equations by appropriate constants to eliminate one variable. The solution to the given system is (1.5, 2).
Step-by-step explanation:
To solve the system of equations 6x - 3y = 3 and -2x + 6y = 14 using the linear combination method, we need to eliminate one of the variables by multiplying the equations by appropriate constants so that the coefficients of one variable become equal in magnitude but opposite in sign. In this case, we will multiply the first equation by 2 and the second equation by 3. This will give us the new system of equations:
12x - 6y = 6
-6x + 18y = 42
Now, we can add the two equations to eliminate the x variable:
(12x - 6y) + (-6x + 18y) = 6 + 42
6y + 18y = 48
24y = 48
y = 2
Substituting the value of y back into the first equation:
6x - 3(2) = 3
6x - 6 = 3
6x = 9
x = 1.5
Therefore, the solution to the system of equations is (1.5, 2).
Learn more about Solving Systems: Introduction to Linear Combinations