# Find the intersection point of the following lines: y = 2x – 3 and y = 2 – 0.5x

October 9, 2021 | education

| To find the intersection points of the straight lines given by the equations y = 2x – 3 and y = 2 – 0.5x, you need to solve the system consisting of the equations of these straight lines. Let’s write down the system,

y = 2x – 3;

y = 2 – 0.5x.

That in the first, that in the second equation we have expressed y through x, we equate the equations and solve for x.

2x – 3 = 2 – 0.5x;

y = 2x – 3.

We solve the first equation of the system.

2x + 0.5x = 2 + 3;

2.5x = 5;

x = 5 / 2.5 = 2.

Now we substitute the value of the variable x = 2 into the second equation of the system and find the value of y:

y = 2 * 2 – 3 = 4 – 3 = 1;

x = 2.

Answer: the point of intersection of the lines has coordinates (2; 1).