How do you solve a 3 term equation?

To solve a system of three equations with three variables, we can use the Addition/Subtraction method. This method involves eliminating one variable at a time by adding or subtracting the equations in the system. Let’s go through the steps using two pairs of equations.

Step 1: Choose two pairs of equations
Let’s say we have the following system of equations:
Equation 1: 2x + 3y – z = 5
Equation 2: x – 2y + 3z = 4
Equation 3: 3x + y + 2z = 1

We can choose any two pairs of equations to start with. For this example, let’s choose equations 1 and 2 as the first pair and equations 1 and 3 as the second pair.

Step 2: Eliminate the same variable from each pair
First Pair: Equations 1 and 2
To eliminate a variable, we need to manipulate the equations so that the coefficients of the variable are opposites. In this case, let’s eliminate the variable x.
Multiply equation 2 by 2:
2(x – 2y + 3z) = 2(4)
2x – 4y + 6z = 8

Now, add equation 1 and the modified equation 2:
(2x + 3y – z) + (2x – 4y + 6z) = 5 + 8
4x – y + 5z = 13

Second Pair: Equations 1 and 3
To eliminate a variable, we need to manipulate the equations so that the coefficients of the variable are opposites. In this case, let’s eliminate the variable x.
Multiply equation 3 by -1:
-1(3x + y + 2z) = -1(1)
-3x – y – 2z = -1

Now, add equation 1 and the modified equation 3:
(2x + 3y – z) + (-3x – y – 2z) = 5 + (-1)
-x + 2y – 3z = 4