How do I decide whether to use Substitution or elimination.??

Question

Examples appreciated

Answer 1

Substitution can be used when working with nonlinear equations, such as x^2 + y = 2, whereas elimination cannot. However, if there are more than two or perhaps three variables and there aren't many coefficients of zero, elimination will result in intermediate equations that are easier to work with. Elimination is also easier to implement in a computer.

Answer 2

Use substitution when is easy to left free the "x"" or the "y" in one side of the equation. example: x+ 3y = 12 , x=12-3y, then substitute this value in the place of every "x" in the other equation.
But if the equation has coefficients in both "x" and "y" you can eliminate them by cross multiplying , example: 2x-3y=8, 3x-4y=6, multiply th first equation by 3 and the second by -2, then eliminate the x and you have -y =12, that is y= -12.

Answer 3

Whichever looks easiest.

3x- 4y = 10
2x +4y =12
Here all you have to do is add the two equations and y is eliminated. So 5x = 22 and x= 4 2/5.

Solving for y and then substituting would be much more cumbersome.

4x -2y =12
x = -y
Here just replace x with -y getting -4y -2y =12 --> y = -2.
This seems easier than elimination.

However as the number of simultaneous equations increases to 3 ,4 and above, elimination is clearly preferable. It is essentially the technique used in matrix solutions.

Answer 4

The idea to remember is that mathemeticians are basically lazy. So they try to do as little dog work as possible. When it comes to simultaneous equations, you substitute when it is convenient to do so, you eliminate when it is convenient to do so. Rules of thumb (AVOID SUBSTITUTION IF THERE ARE FRACTIONS OR DECIMALS. You are more like to make a math error with them)
(DO ELIMINATION IF you have the same absolute coefficient for the x terms or the y terms in both equations. Then you can easily add or subtract. )