After a long day of work, Elliot decides to take a break and read some books. He has 26 books in his collection and he loves reading.
The system of linear equations represents the situation is a system of linear equations that gives the total number of books Elliot has.
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Hi, my name is Elliot and I have a total of 26 books! (I’m not sure how you would multiply the second equation by in order to eliminate, but that’s another story). Anyway, I added the two equations and the result was 2x = 38. So now I know that I have at least one fiction book. And since there are only 26 books, that means that I must also have at least one non-fiction book. But which one? Well, it’s hard to say because there are so many different kinds of books! The drama club is selling short sleeve shirts for $5, so maybe that’s something that I should invest in? Let me know what you think in the comments below!
What number would you multiply the second equation by in order to eliminate?
If you want to eliminate a variable from two equations, you need to multiply one of the equations by a number so that the two equations have the same coefficient for that variable. In this case, if we multiply the second equation by 4, we will get:
4(4x ufffd 9y = 7) ufffd 2x + 3y = 4
16x ufffd 36y = 28 ufffd 2x + 3y = 4
Now we can see that the coefficient for x in both equations is 16, so we can cancel out those terms and solve for y:
16x ufffd 36y = 28
ufffd2x + 3y = 4
14x = 32 (divide both sides by 14) ////This step is incorrect. Dividing by a negative changes the inequality symbol. This should be -14x=-32///// <--See correction below!!!!!!!///////// -14x=-32 (divide both sides by -14) x= 32/14 x= 2.29 (we round up since this is a book count) Therefore, Elliot has 2 fiction books.
Elliot added the two equations and the result was 2x = 38
To solve for x, we need to eliminate one of the variables. In this case, we’ll multiply the second equation by -1 so that both equations have the same y-intercept. This will give us:
4x ufffd 9y = 7
-2x + 3y = -4
After adding these equations together, we get:
2x = 1
Therefore, x = 0.5 and Elliot has half a fiction book.
Solve the equation. How many fiction books does Elliot have?
In order to solve this equation, we need to eliminate one of the variables. In this case, we will multiply the second equation by -1 and add it to the first equation. This will give us a new equation that looks like this: 4x ufffd 9y = 7 ufffd2x + 3y = 4.
Now, we can see that the x terms cancel each other out, leaving us with just a y variable. We can solve for y by adding the two equations together and getting rid of the parentheses. This gives us: 2y = 11. Now we can divide both sides by 2 in order to solve for y. This gives us: y = 5 1/2.
Now that we know what y is equal to, we can plug that back into either of the original equations and solve for x. Let’s use the first equation and plug in 5 1/2 for y. This gives us: 4x ufffd 9(5 1/2) = 7. We can simplify this equation by multiplying 9 and 5 1/2 which gives us 45. So now our equation looks like this: 4x ufffd 45 = 7. We can add 45 to both sides of the equation which will give us 4x = 52 . Finally, we can divide both sides by 4 which will give us x= 13 .
So, Elliot has 13 fiction books
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4x ufffd 9y = 7 ufffd2x + 3y = 4
To solve this equation, you would need to multiply the second equation by -4 and add it to the first equation. This would give you the following:
4x ufffd 9y = 7
-8x + 12y = -16
0x + 3y = -9
From here, you can see that y=3 and x=-3, so Elliot has 3 fiction books.
The “use this system of equations to answer the questions that follow 4x-9y=7” is a book. The author, Elliot, has written 26 books.