Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Answer 1

Answer:

{(-2,3), (7,-6) } -----> y - 15 = -$x^{2}$ + 4x

                               x + y = 1

{(-5, 8). (3,0) } ----> y + 12 = $x^{2}$ + x

                              x + y = 3

{(-2,5),(3,-5) } -----> y + 5 = $x^{2}$  - 3x

                               2x + y = 1

{(2, 3), (8,9)} -----> y-17 = $x^{2}$ - 9x

                              -x + y = 1

Step-by-step explanation:

The simplest way to find the answer is by solving all the equations and finding the value of x and y for each of them.

Solving the equations ->

y + 12 = $x^{2}$  + x

x + y = 3

Substitute y = 3-x from second equation to first and solving the quadratic equation obtained i.e solving $x^{2}$ + 2x -15 = 0 , we get values of x = -5 , 3 and the corresponding values of y by substituting values of x in second equation , y = 8, 0 respectively. So, solution matched  = {(-5, 8). (3,0) }.

Similarly solving other equations using exactly the same method as above we get the following solutions,

For,

y - 15 = $x^{2}$ + 4x

x - y = 1

we don't get any integer solution for this hence it has no match.

For,

y + 5 = $x^{2}$ - 3x

2x + y = 1

we get x = 3,-2 and corresponding y = -5,5

So, solution is {(-2,5),(3,-5) }

For,

y- 6 = $x^{2}$ – 3x

x + 2y = 2

we again don't get any integer solution for x and y so this has no match.

For,

y-17 = $x^{2}$ - 9x

-x + y = 1

we get x = 2,8 and corresponding y = 3,9

So, {(2, 3), (8,9)} is the solution match.

Lastly for,

y - 15 = -$x^{2}$ + 4x

x + y = 1

we get x = -2,7 and corresponding y = 3,6

So, {(-2,3), (7,-6)} is the solution match.