Find the coordinates of the intersection of the graphs y = -0.5x + 2, y = -3 + 1.

To find the point of intersection of the straight lines, which are given by the equations y = -0.5x + 2, y = -3x + 1, we will compose and solve a system of these equations.

So, the system of equations:

y = -0.5x + 2;

y = -3x + 1.

We solve the system using the substitution method. In the first equation, substitute -3x + 1 for the variable y.

System of equations:

-3x + 1 = -0.5x + 2;

y = -3x + 1.

Find the value of the variable x from the first equation:

-3x + 0.5x = 2 – 1;

-2.5x = 1;

We are looking for an unknown factor:

x = 1: (-2.5);

x = -0.4.

System:

x = -0.4;

y = -3 * (-0.4) + 1 = 1.2 + 1 = 2.2.

Answer: (-0.4; 2.2).