A 4-Pack of coffee drinks is $6.90.what is the cost per bottle.
2 answers:
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As an example, let's invert the matrix
We construct the augmented matrix,
On this augmented matrix, we perform row operations in such a way as to transform the matrix on the left side into the identity matrix, and the matrix on the right will be the inverse that we want to find.
Now we can carry out Gaussian elimination.
• Eliminate the column 1 entry in row 2.
Combine 2 times row 1 with 3 times row 2 :
2 (-3, 2, 1, 1, 0, 0) + 3 (2, 1, 1, 0, 1, 0)
= (-6, 4, 2, 2, 0, 0) + (6, 3, 3, 0, 3, 0)
= (0, 7, 5, 2, 3, 0)
which changes the augmented matrix to
• Eliminate the column 1 entry in row 3.
Using the new aug. matrix, combine row 1 and 3 times row 3 :
(-3, 2, 1, 1, 0, 0) + 3 (1, 1, 1, 0, 0, 1)
= (-3, 2, 1, 1, 0, 0) + (3, 3, 3, 0, 0, 3)
= (0, 5, 4, 1, 0, 3)
• Eliminate the column 2 entry in row 3.
Combine -5 times row 2 and 7 times row 3 :
-5 (0, 7, 5, 2, 3, 0) + 7 (0, 5, 4, 1, 0, 3)
= (0, -35, -25, -10, -15, 0) + (0, 35, 28, 7, 0, 21)
= (0, 0, 3, -3, -15, 21)
• Multiply row 3 by 1/3 :
• Eliminate the column 3 entry in row 2.
Combine row 2 and -5 times row 3 :
(0, 7, 5, 2, 3, 0) - 5 (0, 0, 1, -1, -5, 7)
= (0, 7, 5, 2, 3, 0) + (0, 0, -5, 5, 25, -35)
= (0, 7, 0, 7, 28, -35)
• Multiply row 2 by 1/7 :
• Eliminate the column 2 and 3 entries in row 1.
Combine row 1, -2 times row 2, and -1 times row 3 :
(-3, 2, 1, 1, 0, 0) - 2 (0, 1, 0, 1, 4, -5) - (0, 0, 1, -1, -5, 7)
= (-3, 2, 1, 1, 0, 0) + (0, -2, 0, -2, -8, 10) + (0, 0, -1, 1, 5, -7)
= (-3, 0, 0, 0, -3, 3)
• Multiply row 1 by -1/3 :
So, the inverse of our matrix is
Answer:
(14, -2)
Step-by-step explanation:
To solve by using substitution, begin by solving for a variable in the first equation. Let's solve for x:
Now we know what <em>x</em> equals. Let's substitute this into the second equation:
We can then simplify:
Given equation
Combine y terms
Add 2
Divide by -11
So, we now know the value of y = -2.
To find the value of X, we can substitute the value of Y into one of the equations. Let's use the first one:
Substitute for y
Distribute 8
Add 16
So, we now know the value of x = 14.
Therefore, we know a solution to the system of equations is (14, -2).