Question

1) Your friend Taylor missed class today and needs some help identifying solutions of systems. Explain to Taylor where to find the solution(s) of any system using its graph

2)Taylor graphs the following in Desmos and decides that f(x) = g(x) at x = 0, x = 1, & x = 3.

f(x) = 2x+1g(x) = 2x2+1
Provide Taylor some feedback that explains which part of the answer was incorrect and why.

Answer 1

Ques 1:

Let us consider the system of equations,

`2x+y=3` and
`3x-y=2`

It is known that 'The intersection points of the graphs of the system of equations are the solutions of the system of equations'.

So, after plotting the given graphs, we see that from the first graph,

The only intersection point is (1,1).

Thus, the solution of the system is x= 1 and y= 1.

Ques 2:

We have the functions, f(x)= 2x+1 and g(x)= 2x^2+1.

Plotting the graphs of both the functions is shown by graph 2, we see that,

The intersection points are (0,1) and (1,3)

Hence, the function have equal values only at x= 0 and x= 1 but not at x= 3.