Classify each system. the system shown below is . x + 3y = 4 3x + 9y = 12 the system shown below is . 3x – 4y = 12 6x – 8y = 21
2 answers:
Answer:
The first system is consistent & dependent; the second system is inconsistent; and the third system is consistent & independent.
Step-by-step explanation:
A consistent system is a system that has at least one solution. A dependent system is a system that has infinite solutions, because the equations describe the same line. An independent system is a system that has one solution.
An inconsistent system is a system that has no solution because the lines are parallel.
The first system is
To solve this, we would make the coefficients of y the same. We would do this by multiplying the top equation by 3:
We have the same equation; thus this system is consistent and dependent.
The second system is
To solve this, we will make the coefficients of x the same; we will do this by multiplying the top equation by 2:
We have two equations that have the same slope but different y-intercepts; these lines are parallel and thus are inconsistent.
The third system is
To solve this, we will make the coefficients of x the same; we will do this by multiplying the top equation by 3 and the bottom equation by 2:
Now we will add the two equations:
Divide both sides by -5:
-5y/-5 = 40/-5
y = -8
Now substitute this into the first equation:
2x-3(-8) = 8
2x+24 = 8
Subtract 24 from each side:
2x+24 - 24 = 8-24
2x = -16
Divide both sides by 2:
2x/2 = -16/2
x = -8
The solution is (-8, -8); thus the system is consistent and independent.
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<u>Answer:</u>
Sale tax paid by Katrina is 0.44 units of currency and total amount paid is 5.94 unit of currency.
<u> Solution:</u>
Given that Katrina goes to road runner after school and purchase following three products
A soda for 1.50
Chips for 3.50
Candy for 0.50
Also she pays 8% sales tax.
Need to determine amount paid in sales tax and total amount paid by Katrina.
lets first calculate amount she paid without taxes.
Total paid amount without taxes = 1.50 + 3.50 + 0.50 = 5.50
As she paid 8% sale tax , that is 8 % of 5.50
so sale tax paid =
<em>Total amount paid = Total amount paid without taxes + tax paid </em>
= 5.50 + 0.44 = 5.94
Hence sale tax paid by Katrina is 0.44 units of currency and total amount paid is 5.94 unit of currency.
Answer:
Final cost = £779
Step-by-step explanation:
It is given that:
Cost of summer holiday = £650
Amount increased by 11%
Increased cost = 11% of 650
Increased cost =
Increased cost = 0.11 * 650 = £71.50
Amount after increment = 650 + 71.50 = £721.50
Further increase = 8%
Amount = 0.08 * 721.50 = £57.72
Final cost = 721.50 + 57.72 = £779.22
Thus,
Final cost = £779