Question

Activity

The equation y = x + 1 represents plane A and y = -x + 21 represents plane B, where x is the time in minutes and y is the fuel in tons.

Part A
Go to your math tools and open the Graph tool to graph the two sets of equations. To see where the two lines intersect, change the scale so that the x-axis goes from 0 to 30 and the y-axis goes from 0 to 12. Paste a screenshot of the resulting graph in the answer space.



Part B
At which point do the lines intersect?



Part C
Do the coordinates of the point of intersection satisfy both equations simultaneously?

Answer 1

h

Explanation:

Answer 2

Part-A: refer to the attachment

Part-B: (10,11)

Part-C: yes

step-by-step explanation:

Part-A:

refer to the attachment

(I used a online graphing calculator to graph the equations which made the work easy)

Part-B:

When two lines share exactly one common point, they are called the intersecting lines and the point is called the point of interception

Looking at the graph,we can understand that the two lines share a common point at (10,11),

hence,

The lines intercept at the point (10,11)

Part C :

well, to find the answer of this part, we can consider doing equality check by substituting the value of the point we got.

The point (10,11) means that the left and right hand side of both of the equations i.e
`\text{y=x+1 and y=-x+21}` are equal when x and y equal to 10 and 11 respectively.

So let's justify the points:

equation-1:

• y = x + 1

substitute the value of x and y respectively:

• 
  `11\stackrel{?}{=}10+1`

simplify addition:

• 
  `11\stackrel{\checkmark}{=}11`

equation-2:

• y = -x + 21

substitute the value of x and y respectively:

• 
  `11\stackrel{?}{=}-10+21`

simplify addition:

• 
  `11\stackrel{\checkmark}{=}11`

so,

Yes,the coordinates of the point of intersection satisfy both equations simultaneously