find the solution of each equation if the replacement sets are x:{1,3,5,7,9} and y:{2,4,6,8,10}.
3x-9=12
y^2-5y-11=13
3x-9=12
3x = 12+9
3x = 21
x = 7 , which is a member of your solution set
y^2 - 5y - 11 = 13
y^2 - 5y - 24 - 0
(y-8)(x+3) = 0
y = 8 or y = -3
only y=8 is a solution, since -3 is not part of your solution set.
so i don't have to plug in each number?
yes, you could do that.
I don't know what grade level you are at.
The second question involved solving a quadratic.
If you don't know what that is, then plugging in each value of the replacement set would be your way of doing it.
To find the solutions of each equation using the given replacement sets, we substitute each value from the replacement set for the corresponding variable and check if the equation holds true.
Let's start with the first equation:
3x - 9 = 12
For each value of x in the replacement set, substitute it into the equation and solve for x:
For x = 1:
3(1) - 9 = 12
3 - 9 = 12
-6 = 12 (Not true)
For x = 3:
3(3) - 9 = 12
9 - 9 = 12
0 = 12 (Not true)
For x = 5:
3(5) - 9 = 12
15 - 9 = 12
6 = 12 (Not true)
For x = 7:
3(7) - 9 = 12
21 - 9 = 12
12 = 12 (True)
For x = 9:
3(9) - 9 = 12
27 - 9 = 12
18 = 12 (Not true)
Therefore, the only value of x that satisfies the equation is x = 7.
Now let's move on to the second equation:
y^2 - 5y - 11 = 13
Similarly, substitute each value of y from the replacement set into the equation and solve for y:
For y = 2:
2^2 - 5(2) - 11 = 13
4 - 10 - 11 = 13
-17 = 13 (Not true)
For y = 4:
4^2 - 5(4) - 11 = 13
16 - 20 - 11 = 13
-15 = 13 (Not true)
For y = 6:
6^2 - 5(6) - 11 = 13
36 - 30 - 11 = 13
-5 = 13 (Not true)
For y = 8:
8^2 - 5(8) - 11 = 13
64 - 40 - 11 = 13
13 = 13 (True)
For y = 10:
10^2 - 5(10) - 11 = 13
100 - 50 - 11 = 13
39 = 13 (Not true)
Therefore, the only value of y that satisfies the second equation is y = 8.
To summarize:
The solution to the first equation, 3x - 9 = 12, with the given replacement set is x = 7.
The solution to the second equation, y^2 - 5y - 11 = 13, with the given replacement set is y = 8.