Question

Graph and solve the following system:

y = 5x + 3
y = -3x - 5
Use the graphing tool to graph the system. What is the solution?
a) The solution is (4, 7).
b) There are infinitely many solutions.
c) There is no solution.
d) The solution is (-1, -8).

Answer 1

To solve the system, set the two equations equal to each other and solve for x, resulting in x = -1. Substitute x back into one of the equations to get y = -8. Hence, the solution is (-1, -8), which corresponds to answer choice (d).

Step-by-step explanation:

To solve the system of equations y = 5x + 3 and y = -3x - 5, we can set the two equations equal to each other because they both equal y. By doing this, we are looking for an x-value where these two lines intersect on a graph.

To find the x-value, set the equations equal to each other: 5x + 3 = -3x - 5. Combine like terms to get 8x = -8. Dividing both sides by 8 gives us x = -1. We then substitute x = -1 back into one of the original equations to find the y-value. If we use the first equation y = 5x + 3, we get y = 5(-1) + 3, which simplifies to y = -2 + 3, giving us y = -8.

The solution to the system is the intersection point, which is (-1, -8), so the correct answer is (d).