Question

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.

Answer 1

Alright, this is an easy one!

So we are trying to get rid of the y value so the first equation has -3y. The second equation has 2y. What values would make these equal.

A.) 2*-3y = -6y and 3 * 2y = 6y.

Now take -6y + 6y and that gives you 0.

Thus, the answer is A.) Multiply the first equation by 2 and the second equation by 3.

Answer 2

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.

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.