Answer:
Ok, some theory first:
If we have more variables than linear independent equations, then we have infinite solutions.
If we have the same number of linearly independent equations and variables, we can have a unique solution or no solution.
we have no solution in cases where:
y = x + 3
y = x - 3
this leads to:
x + 3 = x - 3
+3 = -3
so this system has no solutions.
The first system of equations is:
y = x + 5
y = 2x + 5
Now, you can see that we have 2 variables, and 2 linear independent equations, this means that we have only one solution for this system
So here we have "One solution, the graph of these lines should intersect at one point" and the point is (0, 5)
The second system is:
y = x + 5 + x = 2x + 5
y = 2x+ 5
Both equations are the same, so here we have 2 variables and only one equation, this means that we have infinite solutions for this system.
here the correct option is the one that says "infinitely many solutions, both right side and left side are equivalent expressions"
