Question

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

Answer 1

Answer with explanation:

The given system of equations :

$x - y = 1-------(1)\\\\-2x + 2y = 5-------(2)$

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

$x - y = 1$

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

At x= 0  , $0 - y = 1\Rightarrow\ y=-1$

At x= 1  , $1 - y = 1\Rightarrow\ y=1-1=0$

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

Now, consider equation (2),

At x= 0  , $- 2(0)+ 2y = 5\Rightarrow\ y=\dfrac{5}{2}=2.5$

At x= 1  , $-2(1)+2 y = 5\Rightarrow\ 2y=5+2\Rightarrow\ y=\dfrac{7}{2}=3.5$

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.