Find all whole number solutions of each system using a table.. 9.) x+y< 8. 3x less than or equal to y+6. .

The correct answers are:

x ≤ 3 and y < 4.

Explanation:

We can isolate the variable y in the first inequality by subtracting x from each side:

x+y < 8

x+y-x < 8-x

y < 8-x

Now we can substitute this into the second inequality:

3x ≤ y + 6

3x ≤ 8-x+6

Combining like terms on the right, we have

3x ≤ 14-x

We will add x to each side so that we only have a variable on one side of the inequality:

3x+x ≤ 14-x+x

4x ≤ 14

Divide both sides by 4:

4x/4 ≤ 14/4

x ≤ 3.5

Now we substitute this into the first inequality:

3.5+y<8

Subtract 3.5 from each side:

3.5+y-3.5 < 8-3.5

y < 4.5

Our solutions are x ≤ 3.5 and y < 4.5.  However, we are asked to find the whole number solutions; this involves some rounding.  While 3.5 would round up to 4, it will not work in our inequality, since x is to be less than or equal to 3.5 and 4 is neither less than nor equal to this number.  Thus we say that x is less than or equal to 3.

4.5 would round up to 5; however, it will not work either, since y is to be less than 4.5 and 5 is not less than 4.5.  Thus we say that x is less than 4.

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