Algebra-2

To find the solution to the system of equations given:

3x + 2y + z = 7

x + y = 4

2z - y = 1  

we will solve these equations step by step.

 

Step 1: Solve the second equation for (y)

From the second equation:

x + y = 4
y = 4 - x

 

Step 2: Substitute (y) into the other equations

Now we will substitute (y = 4 - x) into the first and third equations.

Substitute into the first equation:

3x + 2(4 - x) + z = 7

3x + 8 - 2x + z = 7

 

Combine like terms:

(3x - 2x) + z + 8 = 7

x + z + 8 = 7

 

Now isolate (z):

z = 7 - 8 - x = -1 - x

 

Substitute into the third equation:

Next, substitute (y = 4 - x) into the third equation:

2z - (4 - x) = 1

Expanding this gives:

2z - 4 + x = 1

 

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