# Find the intersection point of the lines given by the equations 3x + 4y + 7 = 0 and 3x-y-5 = 0.

July 21, 2021 | education

| In order to find the point of intersection of the straight lines, which are given by the equations 3x + 4y + 7 = 0 and 3x – y – 5 = 0, we must find a solution to the system of these equations.

system of equations:

3x + 4y + 7 = 0;

3x – y – 5 = 0.

Let us apply the substitution method to the solution. we express the variable y from the second equation in terms of x.

System of equations:

3x + 4y + 7 = 0;

y = 3x – 5.

System of equations:

3x + 4 (3x – 5) + 7 = 0;

y = 3x – 5.

We solve the first equation:

3x + 12x – 20 + 7 = 0;

15x = 13;

x = 13/15;

System:

x = 13/15;

y = 3 * 13/15 – 5 = 13/5 – 25/5 = -12/5 = -2 2/5.