# Find the coordinates of the point of intersection of two straight lines -3x-y + 1 = 0 and 4x + 3y-24 = 0

September 30, 2021 | education

| To find the point of intersection of the straight lines, which are given by the equations -3x – y + 1 = 0 and 4x + 3y – 24 = 0, we must compose and solve the system of equations:

-3x – y + 1 = 0;

4x + 3y – 24 = 0.

Let us express the variable y from the first equation of the system through x and obtain the systems of equations:

y = 1 – 3x;

4x – 3 (1 – 3x) – 24 = 0.

We solve the resulting linear equation:

4x – 3 + 9x – 24 = 0;

4x + 9x = 24 + 3;

13x = 27;

x = 27: 13;

x = 2 1/13.

System of equations:

x = 2 1/13;

y = 1 – 3 * 27/13 = 13/13 – 81/13 = -68/13 = -5 3/13.

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