Consider the system of equations

Question

Consider the system of equation - 2x+3y=8

2x+6y=12

what could be the first step in solving the system of equations using elimination

a. Multiply the first equation by -1

b. Add 4 to both sides of the first equation

c. Add the two equations

d. Multiply the second equation by 2

Answer 1

The first step is always to decide which of the variables, x or y, to eliminate. In this case, the x variable is already set up to eliminate because one equation has 2x, the other -2x. If you add them together, they will eliminate (add to zero). So given that you've decided to eliminate the x, and given that the x terms are already set up to eliminate, the next thing to do would be to add the two equations together. So the answer is (c).

-2x + 3y = 8

2x + 6y = 12

--------------------

0 + 9y = 20

Answer 2

"Elimination" means doing something to the equations so that one variable goes away completely. From there, you can solve for the remaining variable and backtrack to find the eliminated variable. C is the correct choice because when you add the equations, you'd get:

- 2x + 3y + 2x + 6y = 8 + 12

- 2x + 2x + 3y + 6y = 8 + 12 (like terms near each other)

0x + 9y = 20 (combine like terms)

9y = 20 (eliminate 0x)

In other words, adding the -2x and +2x eliminated x entirely, allowing us to solve for y now!

B and D are incorrect because they wouldn't eliminate a variable. A is an okay choice because you could multiply the first equation by -1 and then add the two equations, but this seems longwinded compared to choice C.

Answer 3

add the two equations, which eliminates one variable leaving 9y=20 and y=20/9

then substitute that value into either equation to solve for x= -2/3

C is the correct answer

A,B and D don't get any closer to an answer