Directions; Write a system of equations for each of the descriptions below, and then solve the systems. Hint: you can graph the equations to find the solutions. 16. Three times one number is equal to two times the larger one and their difference is 1. What are the numbers?
17. Joseph has 30 coins and they are all either dimes or nickels. The total $2.15. How many dimes does he have?
18. A golfer completed 18 holes with a total of 79 strokes. On each hole he met par, which was either four or five each time. How many holes were played in four strokes?
19. There are two numbers. The difference between them equals six, and one of the numbers is three times the other number. There are two pairs of numbers that satisfy these descriptions, What are they?
20. There is a number that is three-fifths the total of the other number. When four is added to one of the numbers their sum will be equal to the other number. There are two pairs of numbers that satisfy these descriptions. What are they?

Here are the answers. I walked you through 16 in my answer.

16. 3x=2y

    1 =y-x

x=2 and y=3  

17. $2.15=.10d+.05n

      d=30-n

There are 17 nickels and 13 dimes

18. 18=4x+5y  (since that's the total amount of holes and each par is either 4 or 5 strokes each)

     4x=79-5y  (since there are 79 total strokes and each was either 4 or 5)

No solution

Step-by-step explanation: For each problem, you have to write down the information you know, then define variables for the unknown. For 16, for example, they tell you that one number, which I have chosen to call x, is equal  to two times the larger number, which I have chosen to name y. So, you'd have an equation that equals x. It also tells you that you need three times x, and two times y, which can be rewritten as 3x and 2y. In other words, 3x=2y. That said, you can move on to the next equation. Since you know the difference is 1, in other words, y-x=1, or y=x+1 ( I isolated y by adding x to both sides), you can put that into your equation as well. From there, I used the substitution method to solve.

3x=2y                      

               so          3x=2(x+1)

y=x+1  

3x=2(x+1)                 --- orig equation

3x=2x+2                   --- distributive property (Multiplied x+1 by 2)

x=2                           ---- subtracted 2x from both sides

**Now, to find y, you can substitute x into either equation. Since I know y=x+1 where x=2, I know that y must be 3. To check this, you can graph on Desmos. The lines should intersect at (2,3).

For 18, the lines are parallel so they never intersect. There is no solution.

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step-by-step explanation:

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