Person A buys 10 granola bars and 6 cups of yogurt for <em>$18</em>
Person B buys 5 granola bars and 4 cups of yogurt for <em>$9.50</em>
Let <u>x</u> represent the granola bars
Let <u>y</u> represent the yogurt
10x + 6y = 18 << ( Divide both sides by 2 )
The second equation is 5x + 4y = 9.50. Now subtract the two equations.
5x + 4y = 9.50
-5x - 3y = -9
y = $.50
5x + 3(.50) = 9
5x + 1.50 = 9
5x = 7.5
x = $1.50
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Answer:
<em>Herlene has 8 dimes and 17 quarters</em>
Step-by-step explanation:
<u>System of Equations</u>
Let's call:
x = number of dimes Herlene has
y = number of quarters Herlene has
Since each dime has a value of $0.10 and each quarter has a value of $0.25, the total money Herlene has is 0.10x+0.25y.
We know this amount is $5.05, thus:
0.10x + 0.25y = 5.05 [1]
It's also given the number of quarters is one more than twice the number of dimes, i.e.:
y = 2x + 1 [2]
Substituting in [1]:
0.10x + 0.25(2x + 1) = 5.05
Operating:
0.10x + 0.5x + 0.25 = 5.05
0.6x = 5.05 - 0.25
0.6x = 4.8
x = 8
From [2]:
y = 2*8 + 1 = 17
y = 17
Herlene has 8 dimes and 17 quarters
Let S = number of small yogurts ($2 each).
Let M = number of medium yogurts ($3 each)
Let L = number of large yogurts ($5 each)
Total yogurts is 27, therefore
S + M + L = 27
Total revenue generated is $98, therefore
2S + 3M +5L = 98
There are five more large yogurts than small yogurts, therefore
L = S + 5, or
-S + L = 5
These three equations may be written as the matrix equation
[ 1 1 1 | |S| |27|
| 2 3 5 | |M| = |98|
| -1 0 1 | |L| | 5|
The determinant of the matrix is
D = 3 - (2+5) + 3 = -1.
Solve with Cramer's Rule to obtain
S = -[27*3) - (98-25) - 15]
= 7
M = -[(98-25) - 27(2+5) + (10+98)]
= 8
L = -[15 - (10+98) + 27(3)]
= 12
Answer: 7 small, 8 medium, 12 large yogurts.
the function is decreasing and the y intercept is (0,1)
Answer:

Step-by-step explanation:
A line is a one-dimensional figure that has no thickness and extends infinitely in both directions.
A line segment is a line that has two end-points and a ray is a line that has one end-point.
Given equation is 
To find : a line that lies entirely in the set defined by the given equation.
Solution:
Take 
Check:

Therefore,
satisfy the given equation.