Answer:
The answer that gives the best estimate is (1,1)
Step-by-step explanation:
i) As can be seen on of the lines intercepts the y axis at (0,-1). So the y
intercept or [tex]c_{1}[/tex] = -1. Therefore the equation for this line can be written as
y = [tex]m_{1}[/tex] x + [tex]c_{1}[/tex] ⇒ y = [tex]m_{1}[/tex] x - 1 . It can also be seen from this graph that the
line passes through the point (2 , 2). Substituting these values for x and y
respectively we get 2 = 2[tex]m_{1}[/tex] - 1 ∴ [tex]m_{1}[/tex] = [tex]\frac{3}{2}[/tex]. The equation of the first line
can be written as y = [tex]\frac{3}{2}[/tex] x - 1 ⇒ 2y - 3x = -2
ii) As can be seen on the other line the intercept on the y axis is at (0,2). So
the y intercept or [tex]c_{2}[/tex] = 2. Therefore the equation for this line can be
written as y = [tex]m_{2}[/tex]x + [tex]c_{2}[/tex] ⇒ y = [tex]m_{2}[/tex] x + 2 . It can also be seen from this
graph that the line passes through the point (1 , -1). Substituting these
values for x and y respectively we get 1 = 1[tex]m_{2}[/tex] + 2 ∴ [tex]m_{2}[/tex] = -1 . The
equation of the second line can be written as y = - x + 2 or x + y = 2
iii) Solving the two equations of the two lines respectively as found in i) and
ii) we get y = 0.8. We multiply equation in ii) by 3 to get 3x + 3y = 6 and
when we add this to equation in i) we get 5y = 4 which means that y = 0.8.
If we substitute this value in ii) we get 0.8 + x = 2 , therefore x = 1.2.
iv) Therefore we get the solution of the two lines, which is the intersection
of the two lines as (1.2, 0.8). So the answer that gives the best estimate
is (1,1)
