The system that we need to solve is:
x - y = 6
6x = 12y
And the solution is x = 12 and y = 6.
How to write and solve a system of equations?
Here we first need to define the two variables that we will use, let's define these as x and y.
"The difference between two numbers is 6"
That means:
x - y = 6
"6 times the larger number is 12 times the smaller"
clearly, x is the larger number, thus:
6x = 12y
Then our system of equations is:
x - y = 6
6x = 12y
To solve the system, we first need to isolate one of the variables in one of the equations. I will isolate x on the second one, so we get:
x = 12y/6 = 2y
Replacing that in the other equation, we can get:
x - y = 6
(2y) - y = 6
y = 6
So we know that the smaller number is 6, and the larger number:
x = 2*y = 2*6 = 12
The larger number is 12.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
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