coordinate geometry – straight lines - The lines l_1 with equation y = \frac{3}{2}x -2 and l_2 with equation 2x + 3y = 1 intersect at the point R. (a) Calculate the exact coordinates of R.

Krishna (last edited 3 years ago) (Expert, Educator @Qalaxia)

Step 1: Solve two equations(linear equations in two variables) to find the coordinate (x or y) at the point of intersection

NOTE: If line intersecting the y-axis then put x = 0 in the equation or

If line intersecting the x-axis then put y = 0 in the equation.

EXAMPLE: y = 2x + 3, y = -0.5x + 7

Setting the two y-coordinates equal looks like this:

2x + 3 = -0.5x + 7

2.5x + 3 = 7

2.5x = 4

x = 4/2.5

x = 1.6

You can follow any method to solve the equations.

Step 2: Substitute the coordinator (calculated in step 1) in the either of the equations to find the another coordinate. (x or y)

NOTE: The y-coordinate can be found by placing the x-coordinate, into either of the equations for the lines and solving for y vise versa.

Step 3: You now have the x-coordinate and y-coordinate for the point of intersection.

NOTE: As a check for your work plug the x-coordinate into the other equation and you should get the same y-coordinate.