Question #4782

which method of solving systems of equations is best for you to understand and explain why (substitution or addition). Add an example to your post so other students could understand what you mean.
ex:
2x-3y=6
3x+6y=16

Expert's answer

The universal method of solving linear algebraic systems of equations is extraction and substitution method cause it's the most common method at all. Let's consider an example:

Example:

2x-3y=6& (1)

3x+6y=16 (2)

From (1) we obtain: x = (6+3y)/2.

Substituting x from (1) into (2) we get

3*(6+3y)/2+6y=16

(18+9y)/2+6y=16

9+4.5y+6y=16

10.5y=7

So, y=14/21, and x=(6+3y)/2=(6+3*14/21)/2=3+1=4.

Example:

2x-3y=6& (1)

3x+6y=16 (2)

From (1) we obtain: x = (6+3y)/2.

Substituting x from (1) into (2) we get

3*(6+3y)/2+6y=16

(18+9y)/2+6y=16

9+4.5y+6y=16

10.5y=7

So, y=14/21, and x=(6+3y)/2=(6+3*14/21)/2=3+1=4.

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