Graph each system of equations as a pair of lines in the xy-plane. solve each system and interpret your answer. 19. x - y = 1 - 2x + 2y = 5

The given system of equations :

To plot the given equations of xy plane, we first consider equation (1)

Now, we put some random values of x and note the y values on them

At x= 0  ,

At x= 1  ,

i.e. points to plot equation (1) = (0,-1) and (1,0).

Now, consider equation (2),

At x= 0  ,

At x= 1  ,

i.e. points to plot equation (2) = (0,2.5) and (1,3.5).

Now, we plot the equation as given below, we can see that the lines are parallel lines , also the parallel lines has no intersecting point, it means it has NO SOLUTION.

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.