Explain how to form a linear combination to eliminate the variable y for this system. 2x - 3y = 3
5x + 2y = 17

a) multiply the first equation by 2 and the second equation by 3.
b) multiply the first equation by −5 and the second equation by 2.
c) multiply the first equation by −2 and the second equation by 3.
d) multiply the first equation by 2 and the second equation by −3.

Option (a) is correct.

To form a linear combination to eliminate the variable y for this given system multiply the first equation by 2 and the second equation by 3.

Step-by-step explanation:

Given system of equations,  2x - 3y = 3   and 5x + 2y = 17

We have to form a linear combination to eliminate the variable y for this given system.

Consider the given system

 2x - 3y = 3 (1)  

5x + 2y = 17 (2)

Since, we have to eliminate y from the given system.

This can be done when we make the coefficient of y in both equation same.

So, we Multiply the first equation by 2 and the second equation by 3.

Thus, we get,

 2x - 3y = 3 (1)       × 2

⇒ 4x - 6y = 6   (3 )

5x + 2y = 17 (2)      × 3

⇒ 15x + 6y = 51  (4)

Now , add (3) and (4) , we get,

4x - 6y +(15x + 6y) = 6 + 51

On simplify, we get

20x = 57

Which is completely in terms of x only and y is eliminated.

Thus, To form a linear combination to eliminate the variable y for this given system multiply the first equation by 2 and the second equation by 3.

Option (a) is correct.

the correct answer is 5