Question

The graph of the equation y = -x - 3 is given. Graph y = x + 1 on the grid. What is the solution to this system of equations?

a) A(0, 1)
b) B(5, 6)
c) C(6, 7)
d) D - No solution

Answer 1

To find the solution to the system of equations represented by y = -x - 3 and y = x + 1, graph both lines and find their intersection. Upon solving, the intersection is (-2, -1), which is not listed among the given options; hence, the correct answer is D - No solution.

Step-by-step explanation:

When you are asked to graph the equation y = x + 1 on a grid with an existing line representing y = -x - 3, these two equations form a system. To find their point of intersection, which represents the solution to the system of equations, you would graph both lines on the same grid and see where they cross. The equation y = x + 1 is also linear with a slope (m) of 1 and a y-intercept (b) of 1. You can plot this line by starting at the y-intercept (0,1) and using the slope to find another point, for instance (1,2). To solve for the intersection, set the two equations equal to each other:

-x - 3 = x + 1

Combine like terms to get:

-2x = 4

Divide by -2:

x = -2

Plug x back into either equation to solve for y:

y = -2 + 1 = -1

The solution to the system is (-2, -1), which does not match any of the options provided. Thus, the answer is D - No solution.