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=(5)/(2)=2.5`

At x= 1 ,
`-2(1)+2 y = 5\Rightarrow\ 2y=5+2\Rightarrow\ y=(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.