# How do you solve systems of equations using substitution?

3(5x-2y)=18

5/2x-y=-1

### How do you decide whether to use elimination or subsitution to solve a three-variable system?

There is no simple answer. Sometimes, the nature of one of the equations lends itself to the substitution method but at other times, elimination is better. If they are non-linear equations, and there is an easy substitution then that is the best approach. With linear equations, using the inverse matrix is the fastest method.

### How do you solve systems by using the substitution method?

You solve one of the equation for one of the variables. For example, if the variables involved are "x" and "y", you might solve for "y". It doesn't really matter what variable you solve for first, so you can solve for whatever variable is easiest to solve. Then - assuming you got, for example, "y = 3x -1", in this example you would replace every "y" by "3x - 1" in the other equation or…

### How do you solve mathematical equations using the subsitution method?

Say you have a pair of equations like a+b=1 and 2a+3b=5. To solve using substitution you would set one equation against one variable (say a=1-b) then plug that into the other (2(1-b)+3b=5), then solve for the one variable you have there and then plug that result into the other equation (in this case b=3 and a=-2).

### IF you need to solve large systems with more than three variables which method is more efficient and why?

For systems with more than three equations, Gaussian elimination is far more efficient. By using Gaussian elimination we bring the augmented matrix into row-echelon form without continuing all the way to the reduced row-echelon form. When this is done, the corresponding system can be solved by the back-substitution technique.