Identify the value them make the inequality true x >4 Answers: x=4,x=6,x=10,x= -4
2 answers:
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Given:
The system of equations is
...(i)
...(ii)
To find:
The number that must be multiplied with the second equation to eliminate the y-variable.
Solution:
Coefficient of y variable in equation (i) is 3 and in equation (ii) is -1.
To eliminate y-variable the absolute value of coefficients of y-variables should be same.
So, we need to multiply the second equation by 3 to eliminate the y-variable
Multiplying equation (ii) by 3, we get
...(iii)
Adding (i) and (iii), we get
Divide both sides by 7.
Put x=12 in (i).
Divide both sides by 10.
Therefore, x=12 and y=10.
<u><em>Answer:</em></u>
1. Couples tickets: $8
Individual tickets: $4
2. Song download cost: $2
Movie download cost: $15
<u><em>Step-by-step explanation:</em></u>
You can solve both of these questions by doing system of equations.
Let's start with question 1.
There are 2 variables in this equation:
- Couples tickets price: let's represent these with the letter C
- Individual tickets price: let's represent these with the letter K
Writing the two equations would look this these:
5c + 2k = 48
3c + 2k = 32
Next, isolate a variable. I am going to isolate K in the first equation.
Now that we isolated a variable we can plug that back in to the second equation:
We found that c is equal to 8 so we can put that back in to an equation to solve for k.
5(8) + 2k = 48
40 + 2k = 48
2k = 8
k = 4
Therefore, the price for couples tickets is $8 and the price for individual tickets is $4.
<u><em>Check #1:</em></u>
5(8) + 2(4) = 48
40 + 8 = 48
48 = 48
3(8) + 2(4) = 32
24 + 8 = 32
32 + 32
Now, let's go on to question 2.
There are 2 variables in this equation:
- Price of songs downloaded: let's represent these with S
- Price of movies downloaded: let's represent these with M
Writing the two equations would look like this:
15s + 11m = 195
15s + 8m = 150
There is a simple way to answer this system, however.
If you change the bottom equations signs to negative you can minus the second equation from the first equation like this:
15s + 11m = 195
-(15s +8m = 150)
Minus them to get this equation:
3m = 45
Solve
m = 15
We have found that each movie download costs $15, now let's plug this back into an equation:
15s + 11(15) = 195
15s + 165 = 195
15s = 30
s = 2
Each song costs $2 to download.
<em><u>Check #2:</u></em>
15(2) + 11(15) = 195
30 + 165 = 195
195 = 195
15(2) + 8(15) = 150
30 + 120 = 150
150 = 150
<em>I hope this helps!!</em>
<em>- Kay :)</em>