Tatum wants to solve the following system of equations by using the elimination method. What integer should she multiply the second equation by to eliminate a variable when you add the equations?
6x+3y=14
3x+2y=10
Responses
6
6 - no response given
−2
negative 2 - not selected, this is the correct answer
2
2 - incorrect
−12
-2
show work
To eliminate a variable when adding the equations together, we want to make sure that the coefficients of one of the variables will cancel each other out when the equations are added.
Given the system of equations:
6x + 3y = 14 (Equation 1)
3x + 2y = 10 (Equation 2)
If we multiply Equation 2 by -2, we will get:
-2(3x) -2(2y) = -2(10)
-6x - 4y = -20
Now, we can rewrite the system of equations:
6x + 3y = 14
-6x - 4y = -20
Adding these two equations together, we get:
(6x + 3y) + (-6x - 4y) = 14 - 20
6x - 6x + 3y - 4y = -6
-y = -6
Therefore, multiply the second equation by -2 to eliminate a variable when adding the equations together.