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?

Question

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

a 6
b -1/2
c 2
D -2

GPT-4o mini · Answer

To eliminate a variable using the elimination method, you want to multiply one or both equations so that the coefficients of one of the variables match (or are opposites) when added together.

Let's analyze the given system of equations:

$6 x + 3 y = 14$ (Equation 1)
$3 x + 2 y = 10$ (Equation 2)

To eliminate $x$ , we can compare the coefficients of $x$ in both equations. The coefficient of $x$ in Equation 1 is $6$ and in Equation 2 is $3$ .

To match the coefficients of $x$ , we can multiply Equation 2 by $2$ :

$2 (3 x + 2 y) = 2 (10)$ This gives us: $6 x + 4 y = 20 (New Equation 2)$

Now we can add this modified equation to Equation 1:

$6 x + 3 y = 14$
$6 x + 4 y = 20$

By observing the problem's answer choices, the factor we multiplied the second equation by is $2$ . Thus, the correct answer is:

c 2