solve the following system by the elimination method
x+3y=14
-x+6y=22
To solve the system of equations by the elimination method, we need to eliminate one variable by adding or subtracting the two equations together. Let's eliminate the x variable.
To do this, we'll add the two equations together:
(x + 3y) + (-x + 6y) = 14 + 22
Combine like terms:
x - x + 3y + 6y = 36
9y = 36
Now, let's solve for y by dividing both sides by 9:
9y/9 = 36/9
y = 4
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
x + 3(4) = 14
x + 12 = 14
Subtract 12 from both sides:
x = 2
Therefore, the solution to the system of equations is x = 2 and y = 4.