okay- i definetly don't remember how to do this:
Give an ordered pair(a,b)of numbers that satisfy the equation:
6a+b=8
Common sense says that
a = 1 (6 x 1 = 6)
b = 2
6 + 2 = 8
omigosh.. im dumb.. lol - ok thanks!
No problem! You were on the right track with your approach.
To find an ordered pair (a, b) that satisfies the equation 6a + b = 8, you can choose any value for 'a' and find the corresponding value for 'b' that makes the equation true.
In your example, you chose a = 1, which is a good starting point. Plugging this value into the equation:
6(1) + b = 8
Simplifying:
6 + b = 8
Now, you want to solve for 'b'. Subtracting 6 from both sides of the equation:
b = 8 - 6
b = 2
So, when 'a' equals 1, 'b' equals 2, the ordered pair (1, 2) satisfies the equation 6a + b = 8.
You can also choose other values for 'a' to find different ordered pairs that satisfy the equation. For example, if you choose a = 2, the equation becomes:
6(2) + b = 8
12 + b = 8
Subtracting 12 from both sides:
b = 8 - 12
b = -4
So, when 'a' equals 2, 'b' equals -4, the ordered pair (2, -4) also satisfies the equation 6a + b = 8.
Remember, there are infinite ordered pairs that satisfy the equation, so you can continue to choose different values for 'a' to find more solutions.