b In this diamond we have been given the values of x and y.
&x= 5
&y= -3Let's determine xy and x+y by substituting these values into the expressions.
xy:& 5( -3)=-15
x+y:& 5+( -3)=2
Now we can complete our diamond!
c With the given information we can create the following equations.
x=& 23
xy=& 1
To complete the diamond we should substitute x= 23 in the second equation and find y.
d For the last diamond we can create the following equations.
xy=& -14
x+y=& -5
This tells us that x and y, when multiplied, must give us a negative number. Therefore, either x or y must be negative and the other one must be positive. We have two cases that both results in a product of -14 when multiplied.
-14=-2( 7)
-14= 2(-7)
To determine which pair of integers is correct, we have to check which one sums to-5.
-2 +7 &= 5 & *
2+(-7)&=-5 & ✓
As we can see, the values of x and y are 2 and -7. Now we can complete our diamond!
