Answer:
Part A:
Since the slopes of the lines are not equal, the pair of equations for lines A and B will have one solution.
Part B:
(3 ,5 ) is the solution to the equations of lines A and B.
Step-by-step explanation:
Part A:
We are required to determine the number of solutions that the pair of equations for lines A and B have. To do this, we shall determine the slope of each line;
A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 6, 2. The slope is defined as;
(change in y) / (change in x)
The slope of line A is thus;
(2 - 6)/(6 - 2) = -1
A straight line B joins the ordered pair 0, 3 with the ordered pair 4.5, 6.
On the other hand, the slope of line B is;
(6 - 3) / (4.5 - 0) = 2/3
Since the slopes of the lines are not equal, the pair of equations for lines A and B will have one solution.
Part B:
What is the solution to the equations of lines A and B?
We first need to determine the equation of each line;
Line A, the slope was found to be -1 and the line passes through (2,6)
The equation of the line in slope intercept form is;
y = -x + c
6 = -2 + c
c = 8
y = -x + 8
On the other hand, the slope of line B was found to be 2/3 and the line passes through (0,3). Therefore, we have;
y = 2/3x + c
3 = 2/3 (0) + c
c= 3
y = (2/3)x + 3
The graph of these two lines is shown in the attachment below. The lines intersect at (3 ,5 ) which is the solution to the equations of lines A and B.
The graphical solution to a system of linear equations is given by the point of intersection of the two lines representing each equation.
