For her birthday party, dina wants to invite at least 8 guests but not more than 12 guests. how many guests might she have? name all of the possibilities

This can be represented by the inequality 8 x 12
As Dina wants at least 8, and no more than 12, that means 8, 9, 10,11, and 12, are applicable

Part A

Using substitution method, which means that substitute the value of y from first equation into the second equation, i.e.

7x – 8 = 5x – 2

This implies that;

2x = 6

x = 3

Now putting x = 3 in any equation, because both the equation will give the same value of y,

y = 5(3) – 2

y = 13

or

y = 7(3) – 8

y = 13

Part B

The point of intersection of the two equation graph is actually the solution of both equations. As the value of x = 3 and y = 13, then the point (x, y) = (3, 13) is the point of intersection of both equations.