Question

A pair of equations is shown below: y = 3t − 5 y = 6t − 8 Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points) Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)

Answer 1

Answer:

A)  t = 1, y = -2 is the solution of the given system.

B) The lines representing the two equations will intersect  at (1,-2).

Step-by-step explanation:

Here, the given set of equation are:

y = 3 t -5

and y = 6 t -8

A) Solving the given equations by SUBSTITUTION METHOD, we get

Substitute y = 3t -5 in the equation (2):

we get :  y = 6 t -8  ⇒    3t -5   = 6 t -8

⇒ -5 + 8  = 6t - 3t

or, 3 t = 3

or, t = 3/3  =1

Now, if t = 1, y = 3t -5

                       = 3(1) - 5 = 3 - 5 = -2

Hence, for  t = 1, y = -2 is the solution of the given system.

B) Now, if we plot the graph of both the equations.

The intersection point of the lines of graph is the point which will satisfy both the equations.

And such point from above part is (1,-2).

Hence, the lines representing the two equations will intersect  at (1,-2).