Answer:
All Real Numbers
Explanation:
Hello!
We have to find the intersection of the two lines algebraically using substitution.
Given that y is x + 3, substitute x + 3 for y in the second equation to solve for x.
Solve for x
- 2x - 2y = -6; y = x + 3
- 2x - 2(x + 3) = -6
- 2x - 2x - 6 = -6
- -6 = -6
The solution for x is all real numbers, indicating that the solution to the system is also all real numbers.
What does this mean graphically?
A solution to the system is the point of intersection from all the lines.
If there are infinite solutions (all real numbers), there are an infinite number of intersections, or they are the same line.
Solving for y in the second equation:
- 2x - 2y = -6
- -2y = -2x - 6
- y = x + 3
Both equations are the same.