Question

Consider the following system.

2x - 5y = 6
3x + 2y = 4
If the system was to be solved using elimination, which would be correct factors to multiply each equation by to eliminate the variable x?
A) Multiply the first equation by 2 and the second equation by 3.
B) Multiply the first equation by 3 and the second equation by 2.
C) Multiply the first equation by 5 and the second equation by 2.
D) Multiply the first equation by 2 and the second equation by 5.

Answer 1

The correct method to solve the system using elimination is to multiply the first equation by 3 and the second equation by 2 to eliminate the x variable, which corresponds to option B.

Step-by-step explanation:

To solve the system of equations using elimination, we must multiply the equations by factors that will make the coefficients of one of the variables the same. The equations given are:

• 2x - 5y = 6
• 3x + 2y = 4

Looking at the coefficients of x, which are 2 and 3, we need to find a common multiple. The smallest common multiple of 2 and 3 is 6. To make the coefficients of x the same in both equations, we can:

• Multiply the first equation by 3: (3)(2x) - (3)(5y) = (3)(6), which gives us 6x - 15y = 18
• Multiply the second equation by 2: (2)(3x) + (2)(2y) = (2)(4), which gives us 6x + 4y = 8

Now, both equations have the coefficient of x as 6. By adding or subtracting these new equations, the x variable will be eliminated, allowing us to solve for y.

Therefore, the correct answer is B: Multiply the first equation by 3 and the second equation by 2.