SOLUTION: how would i solve this problem if x = 6 and y = 17 4x + 5y =

Question 685273: how would i solve this problem if x = 6 and y = 17 4x + 5y =
Answer by RedemptiveMath(80) (Show Source): You can put this solution on YOUR website!
You would solve this by simply "plugging" the values 6 and 17 into the spots of x and y (respectively) in the expression "4x + 5y." When we plug something in the place of a variable, or a letter written in place of a certain number that is generally unknown, we usually write parentheses around that number once plugged in as so:

When x = 6 and y = 17 in 4x + 5y, then
4(6) + 5(17).

These parentheses shows us two things. First, it breaks up any confusion caused by not using parentheses. If we just wrote the numbers in place of the numbers, we would have 46 + 517, which this is not correct. Second, it tells us that multiplication is being applied to the number we plugged in. In other words, the number 6 that we plugged in for x is being multiplied by the number next to its parentheses, or the number 4. Similarly, 17 is being multiplied by 5. Parentheses are a short way of showing multiplication in mathematics. To understand why multiplication is used when plugging the numbers in for the variables in this case, look at the final paragraph of this explanation. I'm going to now solve this problem for you.

Now that we have the numbers plugged in and know that 6 is being multiplied by 4 and 17 is being multiplied by 5 (or the other ways around depending on your perspective), we just have to use the order of operations to solve:

4(6) + 5(17) =
24 + 5(17) = (multiplication)
24 + 85 = (multiplication)
109 (addition).

So, the answer to your equation is 109 when x = 6 and y = 17.

Depending on what problems we are working with, multiplication can be used when we plug numbers into the places of variables. One of the times we do this is when a number is front of a variable such as 4x or 5y. This number is called a coefficient. Coefficients are the multipliers in algebra, and the variables are the multiplicands (technical language). 4x is a simple way of writing x being added four times. In other words, x + x + x + x gives the same number as 4 times x, or 4x, no matter what number is plugged into x. 9 + 9 + 9 + 9 = 36, but you also know that 4 times 9 is 36 and 4(9) is 36. This is why we use multiplication when plugging in a number for a variable that has a number before it. It can be called juxtaposing. A number plugged into a variable spot where the variable is written by itself is still being multiplied. For example, x + 9 is equal to 18 when x = 9, but you may see that 9 doesn't change when it is plugged in for x. Or, you may guess that since it doesn't change there is nothing being multiplied. However, x by itself is the same thing as writing 1x. The "1" is just implied. Therefore, 9 is being multiplied by 1, but it doesn't change the 9.

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