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velikii [3]
3 years ago
6

Ann and Ruth bowled together and had a combined score of 410 points. Ann's score was 44 points less than Ruth's score. Write a s

ystem of equations that can be used to determine x, Ann's score and y, Ruth's score.
Mathematics
1 answer:
masha68 [24]3 years ago
3 0

Answer:

x=y-44 and x+y=410

Step-by-step explanation:

So, you want to use the equations x=y-44 and  x+y=410 when x is Ann's score and y is Ruth's score. This is because x (Ann's score) is Ruth's score (y) but 44 less, so you subtract y-44 to get x. Then x+y would also have to equal 410 so that's the other equation. Graphing the 2 equations gets you to the point  (183,227) in which Ann's score is 183 points and Ruth's score is 227 points.

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True or false? A correct answer is worth (2 pts). Explain how you know for the additional (2 pts). Using complete sentence for (
PtichkaEL [24]

<u>answer (in words)</u>

FALSE. the coordinate pair (5, 2) is not a solution to the equation 2x+3y=10. in order to figure out whether or not the statement is true or false, plug the x and y values from the coordinate pair (5, 2) into the given equation, 2x+3y=10. if both sides of the equation end up equal, the coordinate pair is a solution to the equation. if not, the coordinate pair is not a solution to that equation.

<em>(i hope i explained that well enough, i'm better at explaining it algebraically as opposed to putting it into words lol)</em>

<u>answer (algebraic/steps for solving)</u>

first, plug in 5 for x in the equation 2x+3y=10.

  • 2x+3y=10 ⇒ 2(5)+3y=10

then plug in 2 for y.

  • 2(5)+3y=10 ⇒ 2(5)+3(2)=10

now your equation is 2(5)+3(2)=10. all that's left to do is to simplify. you can do this in whatever order you'd like, but i'll start with multiplying 2 · 5.

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multiply 3 · 2.

  • 10 + 3(2) = 10 ⇒ 10 + 6 = 10

add 10 + 6.

  • 10 + 6 = 10 ⇒ 16=10

16 and 10 are <em>not</em> equal, therefore (5, 2) is not a solution to the equation 2x+3y=10. in order for a coordinate pair to be the solution to an equation, both sides of the equation need to end up equal after solving and simplifying.

i hope this helps! have a great rest of your day <3

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