Help me please- Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
1 answer:
<u>Answer:</u>
- One booster pack is worth 9 cards and one premade deck is worth 37 cards.
<u>Step-by-step explanation:</u>
<u>We know that:</u>
- 9x + 7y = 340 cards
- 4x + y = 73 cards
- y = Cost of premade decks (In cards)
- x = Cost of booster packs (In cards)
<u>Work:</u>
- 9x + 7y = 340 cards
4x + y = 73 cards
- 4(9x + 7y = 340 cards)
9(4x + y = 73 cards)
- 36x + 28y = 340 x 4 cards
36x + 9y = 73 x 9 cards
- 19y = 1360 - 657
- 19y = 703
- y = 703/19 = 37
<u>This means that 1 premade deck is worth 37 cards. Now, let's substitute the value of y into the first equation to find x.</u>
- 9x + 7y = 340 cards
- => 9x + 7(37) = 340 cards
- => 9x + 259 = 340 cards
- => 9x = 81 cards
- => x = 9 cards
<u>Hence, one booster pack is worth 9 cards and one premade deck is worth 37 cards.</u>
Hoped this helped.
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Answer:
C. True; by the Invertible Matrix Theorem if the equation Ax=0 has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the n x n identity matrix.
Step-by-step explanation:
The Invertible matrix Theorem is a Theorem which gives a list of equivalent conditions for an n X n matrix to have an inverse. For the sake of this question, we would look at only the conditions needed to answer the question.
- There is an n×n matrix C such that CA=
.
- There is an n×n matrix D such that AD=
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix
- For each column vector b in
, the equation Ax=b has a unique solution.
- The columns of A span
Therefore the statement:
If there is an n X n matrix D such that AD=I, then there is also an n X n matrix C such that CA = I is true by the conditions for invertibility of matrix:
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix
The correct option is C.