To solve the system of equations using the elimination method, we start with the two equations:
1) 2x + 2y = 8
2) x + 2y = 1
First, let’s align both equations for clarity:
Equation 1: 2x + 2y = 8
Equation 2: x + 2y = 1
Our goal is to eliminate one of the variables. To do this, we can first manipulate Equation 2 so that the coefficients of x are the same in both equations. We can achieve this by multiplying Equation 2 by 2:
2*(x + 2y) = 2*1
This results in:
3) 2x + 4y = 2
Now, we can rewrite our system:
1) 2x + 2y = 8
3) 2x + 4y = 2
Next, we subtract Equation 1 from Equation 3 to eliminate x:
(2x + 4y) – (2x + 2y) = 2 – 8
This simplifies to:
2y = -6
Now, we can solve for y:
y = -6 / 2 = -3
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let’s use Equation 2:
x + 2(-3) = 1
x – 6 = 1
x = 1 + 6
x = 7
So, the solution to the system of equations is:
x = 7
y = -3
In summary, by using the elimination method, we found that the values of x and y are:
(x, y) = (7, -3)