Question

6.03

#4
Which system of equations is represented by the graph?

#5
Which system of equations is represented by the graph?

Answer 1

Ques 4)

The system is:

`y=x-4`

`y=(x-4)/(x+2)`

Ques 5)

The system is:

`6x+y=-27`

and
`y=x^2+5x+3`

Explanation:

Ques 4)

After looking at the graph we observe that :

The first graph is a line which passes through (4,0) and (0,-4)

Hence, the equation of such a line is:

y=x-4

and the second graph is a curve such that the vertical asymptote is at x= -2

and also x= 4 is a root of the rational function.

Since, the graph passes through (4,0)

Hence, the system equation which best represents the graph is:

`y=x-4`

`y=(x-4)/(x+2)`

Ques 5)

One of the curve is :

a line that passes through (-5,3) and (-6,9)

Hence, the equation of line is given by:

`y-3=(9-3)/(-6-(-5))* (x-(-5))\\\\i.e.\\\\y-3=(6)/(-6+5)* (x+5)\\\\i.e.\\\\y-3=(6)/(-1)* (x+5)\\\\i.e.\\\\y-3=-6(x+5)\\\\i.e.\\\\y-3=-6x-30\\\\i.e.\\\\y=-6x-30+3\\\\i.e.\\\\y=-6x-27`

i.e. Equation of line is:

`6x+y=-27`

While the other graph is a upward facing parabola such that the vertex is in third quadrant this means that the coefficient of x^2 must be positive and that of x must also be positive.

Hence, the system in which the equation of line satisfies is:

`6x+y=-27`

and
`y=x^2+5x+3`