Question

Match each statement with its corresponding value for the system below:

y = -2(3)x and y = 9x - 2

1. The number of points of intersection.
2. The x-coordinate of the solution.
3. The y-coordinate of the solution.

Answer 1

1. 1 point

2. The x-coordinate of the solution = 2/17

3. The y-coordinate of the solution = -16/17

Explanation:

Given that the equation is of the form;

y = -2³×x and y = 9·x - 2, we have;

y = -8·x and y = 9·x - 2

1. Given that the two lines are straight lines, the number of points of intersection is one.

2. The x-coordinate of the solution

To find a solution to the system of equations, we equate both expression of the functions and solve for the independent variable x as follows;

-8·x = 9·x - 2

-8·x - 9·x= - 2

-17·x = -2

x = 2/17

The x-coordinate of the solution = 2/17

3. The y-coordinate of the solution

y = 9·x - 2 = 9×2/17 - 2 = -16/17

y = -16/17

The y-coordinate of the solution = -16/17.