# How do you solve using the elimination method #3x + 4y = 5#, #6x + 8y = 10#?

##### 1 Answer

This system of equations has an *infinite number of solutions*.

#### Explanation:

Your system of equations looks like this

#{(3x + 4y = 5), (6x + 8y = 10) :}#

Notice that if you multiply the first equation by

#{(3x + 4y = 5 | * (-2)), (6x + 8y = 10) :}#

#{(-6x - 8y = -10), (6x " "+ 8y = " "10) :}#

#stackrel("---------------------------------------------")#

#" "0 " "+ 0 " "= 0#

Since you end up with **infinite number of solutions**.

You can think of a system of equations as describing *two lines*. In your case, both equations decribe the **same line**, because if you multiply the first equation by

#{(6x + 8y = 10), (6x + 8y = 10) :}#

This implies that you have an infinite number of