Answer:
Explanation:
When you have a system of linear equations with three or more variables, you can use various methods to solve for the values of those variables. In this case, you have a system of three linear equations with three variables (x, y, and z):
1. 2x - 3y + z = 9
2. -2x + y - 3z = 7
3. x - y + 2z = -5
One common method to solve such a system is using the technique of elimination or substitution. Here's a step-by-step process using elimination:
Step 1: Choose two equations and eliminate one variable. You'll want to choose equations that, when combined, eliminate one of the variables.
Let's start with equations (1) and (2). If we add these two equations, the x terms will cancel out:
(2x - 3y + z) + (-2x + y - 3z) = 9 + 7
This simplifies to:
-2y - 2z = 16
Step 2: Solve the equation obtained in step 1 for one variable. In this case, we can solve for y:
-2y - 2z = 16
-2y = 16 + 2z
y = -8 - z
Step 3: Substitute the expression for y into one of the original equations to solve for another variable. Let's substitute it into equation (3):
x - (-8 - z) + 2z = -5
x + 8 + z + 2z = -5
x + 3z + 8 = -5
Step 4: Solve for x:
x + 3z + 8 = -5
x + 3z = -5 - 8
x + 3z = -13
Now, you have expressions for y and x in terms of z:
y = -8 - z
x = -13 - 3z
This represents a solution in terms of the parameter z. You can choose specific values for z and then find the corresponding values of x and y to obtain different solutions to the system.
Keep in mind that this is a system of linear equations, so there can be infinitely many solutions, and you may choose different strategies or equations to work with depending on the specific problem and what you want to find.