1. 1 point
2. The x-coordinate of the solution = 2/17
3. The y-coordinate of the solution = -16/17
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.
As, we can see the graph, the two lines intersect at exactly one point. Hence, there is just one solution.
Theortically, As the slope of and is different. Hence, the system of equation has exactly one unique solution.
2. The x coordinate of the solution from graph is 0.1333.
Theortically, From, y=-2(3x) and y=9x-2
Adding 2 on both sides, we get,
Adding 6x on both sides, we get,
Dividing by 15 on both sides
As, x=0.1333 in y=-2(3)x
Graphically, as well y coordinate of point of intersection is -0.8
I graphed both functions and the answer should be the following:
Number of points of intersection = 1
x - coordinate of the solution = 0
y - coordinate of the solution = (-2)
hope this helps you!