Algebra-2

Given System of Equations

1.( x + 2y = 6 )  (Equation 1)

2.( 3x - y + z = 7 )  (Equation 2)

3.( 2x + 4y - 3z = 3 )  (Equation 3)

 

Step 1: Multiply Equation 2 by 3

First, we multiply Equation 2 by 3 to facilitate the elimination of (z):

3(3x - y + z) = 3(7)

This yields:

9x - 3y + 3z = 21 {Equation 4}

 

Step 2: Add Equation 4 to Equation 3

Now, we add Equation 4 to Equation 3 to eliminate (z):

(9x - 3y + 3z) + (2x + 4y - 3z) = 21 + 3

 

This simplifies to:

(9x + 2x) + (-3y + 4y) + (3z - 3z) = 24

Thus:

11x + y = 24 {Equation 5}

 

Step 3: Solve for (y) in terms of (x)

Now we can express (y) in terms of (x) from Equation 5:

y = 24 - 11x {Equation 6}

 

Step 4: Substitute (y) into Equation 1

Next, we substitute (y) from Equation 6 into Equation 1 to solve for (x):

x + 2(24 - 11x) = 6

x + 48 - 22x = 6

-21x + 48 = 6

 

Step 5: Isolate (x)

Now, isolate (x):

-21x = 6 - 48

-21x = -42

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