Write down the equations for the two lines. Consider the following example:
Line 1: y = 2x + 4
Line 2: y = x - 3
Solve for x by substituting what y equals in one line for the "y" in the other line. In this example, y equals 2x + 4 in line 1. Substitute this in place of y for line 2 as follows: 2x + 4 = x - 3. Group like terms and change the signs of any terms that you move across the equal sign. In this example, you would bring the x to the left of the equation and the 4 to the right of the equation, which would look like this: 2x - x = -3 + -4. Solve for x. In this example, 2x - x equals x, and -3 + - 4 equals -7. The final solution is x = -7. Therefore the x coordinate for the point of intersection is -7.
Solve for y by substituting what x equals in one line for the "x" in the other line. In this example, you can rearrange the equation for the second line to determine what x equals. The equation of the second line is y = x - 3. Move the -3 to the other side of the equation and change its sign, so that you have y + 3 = x. Since x equals y + 3, substitute this for x in the other line as follows: y = 2 (y + 3) + 4. Simplify to solve for y. In this case you would multiply 2 times (y + 3) to get y = 2y + 6 + 4. Move 6 and 4 to the left side of the equation and y to the right side, changing signs as you cross the equals sign. Then you would have
-6 + -4 = 2y - y. This simplifies to -10 = y, or y = -10. Therefore the y coordinate for the point of intersection is -10 in this example.
Write your answer as a set of coordinates. Write the x coordinate first. Separate the coordinates with a comma and place them in a set of parentheses. In this example, you would write (-7, -10).