Answer:
To solve this system of equations, we need to find the x-values where the two equations intersect on a graph.
The first equation, y = x + 2, has a y-intercept of 2 and a slope of 1. This means that for every increase of 1 in x, y increases by 1. We can plot this line on a coordinate plane by plotting the y-intercept at (0, 2) and then using the slope to find another point, such as (1, 3), and drawing a line through those two points.
The second equation, y = 2x + 1, has a y-intercept of 1 and a slope of 2. This means that for every increase of 1 in x, y increases by 2. We can plot this line on the same coordinate plane by plotting the y-intercept at (0, 1) and then using the slope to find another point, such as (1, 3), and drawing a line through those two points.
Now we can see where the two lines intersect on the graph. This occurs at the point (−1,1). Therefore, the first answer choice, "x = -1 and x = 2," is not correct.
The second answer choice, "x = 1 and x = 2," is also not correct, as we can see from the graph that the two lines do not intersect at x = 1.
The third answer choice, "x = 0 and x = 1," is also not correct, as we can see from the graph that the two lines do not intersect at x = 0.
The only remaining answer choice is "x = -2 and x = -3," and we can see from the graph that the two lines do intersect at x = -2. Therefore, the correct answer is "x = -2 and x = -3."