solve by addition method
x +3y +z =6
3x + y – z = -2
2x +2y – z = 1
thanks
To solve this system of equations using the addition method, you need to eliminate a variable by adding or subtracting the equations. Here's how:
Step 1: Choose two equations and decide which variable you want to eliminate first. In this case, let's eliminate the variable "z".
Step 2: Multiply one or both equations by a number so that the coefficients of "z" in both equations are the same. We can achieve this easily by multiplying Equation 1 by 1 and Equation 2 by -1.
Original Equations:
Equation 1: x + 3y + z = 6
Equation 2: 3x + y - z = -2
Modified Equations:
Equation 1': x + 3y + z = 6 (no change)
Equation 2': -3x - y + z = 2
Step 3: Add Equation 1' and Equation 2' to eliminate "z". This will give us a new equation.
Equation 1' + Equation 2': x -3x + 3y - y + z - z = 6 + 2
-2x + 2y = 8
Step 4: Simplify the new equation obtained to get a single equation in terms of two variables.
-2x + 2y = 8
Step 5: Now we need to eliminate another variable. Choose a different pair of equations and decide which variable you want to eliminate next. Let's eliminate "z" again.
Step 6: Multiply one or both equations by a number so that the coefficients of "z" in both equations are the same. This time, we'll multiply Equation 2 by 1 and Equation 3 by -1.
Original Equations:
Equation 2: 3x + y - z = -2
Equation 3: 2x + 2y - z = 1
Modified Equations:
Equation 2': 3x + y - z = -2 (no change)
Equation 3': -2x - 2y + z = -1
Step 7: Add Equation 2' and Equation 3' to eliminate "z". This will give us another new equation.
Equation 2' + Equation 3': 3x - 2x + y - 2y - z + z = -2 - 1
x - y = -3
Step 8: Simplify the new equation obtained to get a single equation in terms of two variables.
x - y = -3
Step 9: Now we have two equations:
-2x + 2y = 8
x - y = -3
You can solve this system of linear equations using different methods such as substitution, elimination, or matrix methods.