To find the solution to the system of linear equations:
- Equation 1: 2x + y = 1
- Equation 2: 3x + y = 6
We can solve this system using the substitution or elimination method. Here, we’ll use the elimination method:
Step 1: Align the equations
Let’s write both equations clearly:
1) 2x + y = 1 2) 3x + y = 6
Step 2: Eliminate one variable
We can eliminate y by subtracting Equation 1 from Equation 2:
(3x + y) - (2x + y) = 6 - 1
Which simplifies to:
3x - 2x = 5
This results in:
x = 5
Step 3: Substitute x back into one of the original equations
Now that we have the value of x, we can substitute it back into either Equation 1 or Equation 2. Let’s use Equation 1:
2(5) + y = 1
Which simplifies to:
10 + y = 1
Solving for y gives:
y = 1 - 10
y = -9
Step 4: Write the solution
We have found the values of x and y:
The solution to the system of equations is: (x, y) = (5, -9)
Conclusion
The solution to the equations 2x + y = 1 and 3x + y = 6 is (5, -9). This means that when x is 5, y will be -9, satisfying both equations.