Solve the system of equation
y =x −2
y =4x+1

This is called system of equations because you are searching a pair of numbers that inserted as

x

and

y

verify both equations at the same time.

To solve a system of equation you have to use one equation to express one variable as a function of the other, and substitute the result in the second equation.

In your case you have

y

=

x

−

2

So your

y

variable will be always equal to

x

−

2

, even in the second equation. Then we can write

x

−

2

=

4

x

+

1

Here I replaced the "value" of

y

in the second equation.

Now you have an equation in one variable that you can solve as usual

x

−

2

=

4

x

+

1

4

x

−

x

=

−

2

−

1

3

x

=

−

3

x

=

−

1

With a value for

x

you can substitute in one of the two equations and obtain

y

. Because both equations has to be valid at the same time, both equations must give you the same number for

y

. Let's try:

y

=

x

−

2

y

=

−

1

−

2

y

=

−

3

and, with the second equation

y

=

4

x

+

1

y

=

4

(

−

1

)

+

1

y

=

−

4

+

1

y

=

−

3

.

It works! Then our solution is given by

x

=

−

1

and

y

=

−

3

.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50