When using an elimination strategy to solve the system 3a^2=17-5t and
7a+24=3a^2-2t, the variable that can be eliminated is
A. a
B. a^2
C. t
D. an elimination strategy cannot be used with this system
omg i waited for a good 2 minutes before I realized hahaha
reformatting the equations, you have
3a^2 + 5t = 17
3a^2-7a-2t = 24
eliminating t, you have
6a^2 + 10t = 34
15a^2-35a-10t = 120
21a^2 - 35a - 154 = 0
3a^2 - 5a - 22 = 0
solve as usual for a, then find t
To determine which variable can be eliminated using the elimination strategy, we need to examine the two equations provided:
Equation 1: 3a^2 = 17 - 5t
Equation 2: 7a + 24 = 3a^2 - 2t
Looking at the equations, we notice that both equations contain a term with a^2. This suggests that the a^2 variable can be eliminated using the elimination strategy.
Therefore, the answer is B. a^2.
To determine which variable can be eliminated using an elimination strategy, we need to check if there is a coefficient of the same variable in both equations.
Let's analyze the system of equations:
1) 3a^2 = 17 - 5t
2) 7a + 24 = 3a^2 - 2t
In equation 1, we have a^2 with a coefficient of 3. On the other hand, equation 2 also has a^2 but with a coefficient of 3. Since they have the same coefficient, we can eliminate a^2 by subtracting equation 2 from equation 1:
3a^2 - (3a^2 - 2t) = 17 - 5t - (7a + 24)
Simplifying this, we get:
3a^2 - 3a^2 + 2t = 17 - 5t - 7a - 24
2t = -5t - 7a - 7
The variable a remains in the equation, and the variable t remains as well. However, we can eliminate one of them. By rearranging the equation, we can isolate either a or t. Let's isolate t:
2t + 5t = -7a - 7
7t = -7a - 7
t = (-7a - 7) / 7
t = -a - 1
Therefore, the variable that can be eliminated using an elimination strategy is t. So the answer is C. t.