To solve the system of equations:
- 2x + y = 3 (1)
- x + 2y = 1 (2)
We can use the method of substitution or elimination. Here, we’ll use the elimination method.
First, we can rearrange equation (1) for y:
y = 3 – 2x
Next, we substitute this expression for y into equation (2):
x + 2(3 – 2x) = 1
x + 6 – 4x = 1
-3x + 6 = 1
-3x = 1 – 6
-3x = -5
x = 5/3
Now that we have the value of x, we can substitute it back into the rearranged equation for y:
y = 3 – 2(5/3)
y = 3 – 10/3
y = 9/3 – 10/3
y = -1/3
Thus, the solution to the system of equations is:
x = 5/3 and y = -1/3