Which of the following would be the best first step to solve the system of equations? 2x – 9y = 6. 4x – 3y = –7 a. multiply the first equation by 2.. b. multiply the second equation by 2.. c. multiply the first equation by –3. d. multiply the second equation by –3.

The answer is  D. Multiply the second equation by –3.

Let's try all choices:
A. Multiply the first equation by 2.
2x – 9y = 6     -multiply by 2
4x – 3y = –7  

4x - 18y = 12
4x - 3y = -7
After adding this two equations:
4x - 18y + 4x - 3y = 12 + (-7)
8x - 21y = 5                - still have both x and y

B. Multiply the second equation by 2.
2x – 9y = 6     
4x – 3y = –7    -multiply by 2

2x – 9y = 6
8x - 6y = -14
After adding this two equations:
2x – 9y + 8x - 6y  = 6 + (-14)
-7x + 2y = -8              - still have both x and y

C. Multiply the first equation by –3
2x – 9y = 6     -multiply by -3
4x – 3y = –7  

-6x + 27y = -18
4x - 3y = -7
After adding this two equations:
-6x + 27y + 4x - 3y  = -18 + (-7)
-2x + 24y = -25               - still have both x and y

D. Multiply the second equation by -3.
2x – 9y = 6     
4x – 3y = –7    -multiply by -3

2x – 9y = 6
-12x +9y = 21
After adding this two equations:
2x – 9y + -12x +9y  = 6 + 21
-10x = 27
So, there is only x to solve.