Solve the equation system of equations 2x + 3y = 10 -2x + 5y = 6 using addition.

To calculate a pair of numbers that are the solution to the system:

2x + 3y = 10;

-2x + 5y = 6,

we are asked to use the addition method. And after considering both equations, we see that the variable x is preceded by mutually opposite coefficients.

We proceed directly to the addition of the two equations of the system and we get:

2x = 10 – 3y;

3y + 5y = 10 + 6,

Let’s solve the resulting equation with one variable:

3y + 5y = 10 + 6;

8y = 16;

y = 2.

System:

x = (10 – 3y) / 2;

y = 2.

Substitute the found value for y into the first equation.

System:

x = (10 – 6) / 2 = 4/2 = 2;

y = 2.