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Three times one number is 24 more than twice another number. The sum of the numbers is eleven times their difference. Find the numbers.

Answer :

Taking into account the definition of a system of linear equations, the numbers are 18 and 15.

System of linear equations

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, when the values of the unknowns are replacing, they must give the solution proposed in both equations.

This case

In this case, a system of linear equations must be proposed taking into account that "x" and "y" are two numbers. Being:

  • Three times one number is 24 more than twice another number.
  • The sum of the numbers is eleven times their difference.

The system of equations to be solved is

3x= 2y +24

x + y= 11(x-y)

The graphic method consists of representing the graphs associated with the equations of the system, with the solution of the system being the point of intersection between the graphs, since the coordinates of said point satisfy both equations.

In this case, graphing both equations (attached graph) shows that the solution is the point (18,15). So, the numbers are 18 and 15.

Learn more about system of equations:

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