Examine the system of equations. t = 5c + 35, t = 10c How many solutions will the system have? What is the reason you determined that number of solutions?

(1)  t = 5c + 35  

(2) t = 10c

(a) Create a table containing a few values of x and y

 t    5c + 35  10c  

 0        35          0

 2        45        20

 4        55        40

 6        65        60

 8        75        80

10         85      100

(b) Draw your axes

You should scale your axes so the graph covers most of the plot area.

The slopes of your lines are so steep that, without scaling, they will be quite steep, and it will be difficult to tell where they intersect.

The independent variable is c, so the c-axis is horizontal. The dependent variable is t, so it goes on the vertical axis.

Let the c-axis run from -2 to 12 and the t-axis from -20 to 120.

Divide the axes into convenient intervals for ease of reading (I chose units of 2 for the c-axis and 20 for the t-axis).

(2) Plot your points

Draw dots at the coordinates of each point.

(3) Draw the graphs

Draw straight lines through the points.

Extend the line in both directions to the edges of the plot area.

Your graph should look like the figure below.

With the scaled axes, it is easy to see that the two lines intersect at (7, 70).

Step-by-step explanation:

Ik it's super late but for others this is the answer.

one solution

The equations graph intersecting lines.

2222222222222222222

step-by-step explanation:

c.35

step-by-step explanation:

8+13=21

21+8=29

29+6=35