Question

A system of linear equations is graphed. which ordered pair is the best estimate for the solution to the system?

Answer 1

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 $c_{1}$ = -1. Therefore the equation for this line can be written as

 y = $m_{1}$ x + $c_{1}$    ⇒    y = $m_{1}$ 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$m_{1}$ - 1    ∴ $m_{1}$ = $\frac{3}{2}$.  The equation of the first line

 can be written as y = $\frac{3}{2}$ 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 $c_{2}$ = 2. Therefore the equation for this line can be  

  written  as  y = $m_{2}$x + $c_{2}$    ⇒    y = $m_{2}$ 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$m_{2}$ + 2    ∴ $m_{2}$  = -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)