Find the point of intersection of the graphs of linear functions y = 5x + 1 and -3x + 4

In order to find the point of intersection of the graphs of linear functions given by the equations y = 5x + 1 and y = -3x + 4, we solve a system of these equations.

System of equations:

y = 5x + 1;

y = -3x + 4.

We will solve the system by the substitution method. Substitute -3x + 4 for y in the first equation.

System of equations:

-3x + 4 = 5x + 1;

y = -3x + 4.

We solve the first equation of the system:

-3x – 5x = 1 – 4;

-8x = -3;

x = -3: (-8);

x = 3/8.

System of equations:

x = 3/8;

y = -3 * 3/8 + 4 = -9/8 + 32/8 = 23/8.

Answer: (3/8; 2 7/8).