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).
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