# Find the abscissa of the point of intersection of the graphs of two linear equations

October 12, 2021 | education

| **Find the abscissa of the point of intersection of the graphs of two linear equations with two variables 4x-3y = 12 and 3x + 4y = -24**

If the graphs overlap, then their equations have a common solution. Because it is necessary to find the abscissa, therefore it is necessary to determine at which x the equalities are satisfied:

4x – 3y = 12,

3x + 4y = -24.

From the first equality we find 3y = 4x – 12, y = (4x – 12) / 3.

We get:

3x + 4 (4x – 12) / 3 = -24,

3x + (16x – 48) / 3 = -24,

9x + 16x – 48 = -72,

25x = -24,

x = -24/25.

or x = – 0.96.

Answer: the abscissa of the intersection point x = -0.96.

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