Final answer:
The solution set of the given system of equations y = 3x + 10 and 2y = 6x – 4 is empty, indicating that the lines are parallel and do not intersect.
Step-by-step explanation:
To find the solution set of the system of equations y = 3x + 10 and 2y = 6x – 4, we can solve the equations simultaneously by substitution or elimination method.
Using the substitution method:
- Step 1: Substitute the value of y from the first equation into the second equation. 2(3x + 10) = 6x – 4.
- Step 2: Simplify the equation: 6x + 20 = 6x – 4.
- Step 3: Combine like terms and isolate the variable: 6x - 6x = -4 - 20.
- Step 4: Simplify further: 0 = -24.
- Step 5: Since 0 does not equal -24, the system of equations does not have a solution.
Therefore, the solution set of the system of equations y = 3x + 10 and 2y = 6x – 4 is empty, indicating that the lines represented by the equations do not intersect and are parallel.