slove using substitution

Question

can you please show me step by step on solving this using substitution   x-2y=-5 and 2x-3y=-3 i am really trying it is so hard

Answer 1

Nick,

Substitution is about replacing an item of equal value... It's like with coffee: some people like sugar, but there are others who substitute with "Equal" because of the calories.  The result is the same, because both products sweeten the coffee.  One can be used in place of the other.

 

x - 2y = - 5

2x - 3y = - 3

 

The key here is looking for a variable (one of the letters) that has no coefficient.  It is just a variable all by itself with no number in front of it.  See the "x" in the first equation?  That's the one we want to focus on.

 

It is possible to get "x" all by itself by adding 2y (opposite math) to both sides of the equation:

 

x - 2y + 2y = - 5 + 2y

 

The result:

 

x = - 5 + 2y

 

This is helpful because even though we don't know what number "x" is, we do know that it has the same value as "- 5 + 2y".  If these are equal, then just like the coffee sweeteners, either one can be used.  We just have to substitute "x" for "- 5 + 2y" in the other equation:

 

x = - 5 + 2y

2x - 3y = - 3

 

2(- 5 + 2y) - 3y = - 3

 

Here I have replaced (substituted) "x" with "- 5 + 2y" instead.  This is helpful because now the equation only has one type of variable: y.

 

2(- 5 + 2y) - 3y = - 3

 

Distribute the 2:

 

- 10 + 4y - 3y = - 3

 

Combine like terms (y terms):

 

- 10 + 1y = - 3

 

Use opposite math to remove the - 10 (add 10 to both sides):

 

- 10 + 10 + 1y = - 3 + 10

 

1y = 7   or   y = 7

 

Yey!!  Now you have a solution for "y" and can use it to go back and find the numerical value of "x", by substituting.

 

Remember, x = - 5 + 2y.  So, x = - 5 + 2(7) = - 5 + 14 = 9

 

The final solution to the problem is written as (x, y):  (9, 7)