Algebra-2

To find the solution to the system of equations given:

3x + 2y = 6

x - y = 1

2x + y - z = 4

we will solve the first two equations for (x) and (y) first, and then we will use those values to find (z).

 

Step 1: Solve the first two equations

From the second equation, we can express (x) in terms of (y):

x - y = 1
x = y + 1

Substitute (x) into the first equation:

 

Now substitute (x = y + 1) into the first equation:

3(y + 1) + 2y = 6

This expands and simplifies to:

3y + 3 + 2y = 6

 

Combining like terms gives:

5y + 3 = 6

Subtracting 3 from both sides:

5y = 3

 

Now, substitute (y) back into the equation for (x):

So we have:

 

Step 2: Find (z) using the third equation

Now substitute and into the third equation:

2x + y - z = 4

Substituting for (x) and (y):

This simplifies to:

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