Answer:
1. To find the solution for the given system of equations, we can use the method of substitution or elimination. Let's start by using the substitution method. From the first equation, we can express x in terms of y as x = 2 + 2y. Substituting this value of x into the second equation, we get 3(2 + 2y) - 5y = 2. Simplifying this equation, we have 6 + 6y - 5y = 2, which further simplifies to y = -4.
2. Now that we have found the value of y, we can substitute it back into either of the original equations to find the value of x. Let's substitute y = -4 into the first equation, x - 2(-4) = 2. Simplifying this equation, we get x + 8 = 2, which gives x = -6.
3. Therefore, the solution to the system of equations x - 2y = 2 and 3x - 5y = 2 is x = -6 and y = -4. This means that the two equations intersect at the point (-6, -4) on the coordinate plane.