Solve a system of linear equations with two variables, addition method 2x-y = 13 2x + 3y = 9.

To find a solution to the system of equations:

2x – y = 13;

2x + 3y = 9,

we will apply the addition method as suggested in the statement of work.

First of all, we will consider both equations of the system and determine which equation we must multiply and by what number, so that in front of one of the variables we get mutually opposite coefficients.

So, multiply the first equation of the system by -1:

-2x + y = -13;

2x + 3y = 9.

Let us add the two equations of the system and write it down instead of the second:

2x = 13 + y;

y + 3y = 9 – 13.

We solve the resulting second equation of the system:

4y = -4;

y = -1.

System of equations:

x = (13 + y) / 2 = (13 – 1) / 2 = 12/2 = 6;

y = -1.