Question

Which of these strategies would eliminate a variable in the system of equations? \begin{cases} 6x + 5y = 1 \\\\ 6x - 5y = 7 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ 6x+5y=1 6x−5y=7 ​ Choose all answers that apply: Choose all answers that apply: (Choice A) A Add the equations. (Choice B) B Subtract the bottom equation from the top equation. (Choice C) C Multiply the top equation by 777, then subtract the bottom equation from the top equation.

Answer 1

To eliminate a variable in the system of equations, you can add or subtract the equations. Both choices A and B will eliminate the variable 'y'.

Step-by-step explanation:

To eliminate a variable in a system of equations, you can use one of two methods: adding or subtracting the equations. In this case, both choices A and B would eliminate the variable 'y'.

(Choice A): Adding the equations:

6x + 5y = 1
6x - 5y = 7

When you add the equations term by term, the 'y' terms cancel out:
12x = 8

So, the variable 'y' is eliminated.

(Choice B): Subtracting the equations:

6x + 5y = 1
- (6x - 5y = 7)

When you subtract the second equation from the first equation, the 'y' terms cancel out:
2y = -6

So, the variable 'y' is eliminated.

Answer 2

Option A and B are correct

Step-by-step explanation:

We have to add here

6x+5y=1.

6x-5y=7

sow e will get 12x=8 , x=8/12=2/3

Option A is correct.

If We substract bottom from furst then

6x+5y=1

-6x+5y=-7

10y=-6

y=-6/10=-3/5

we put y=-3/5 in any equation and find x

6x+5(-3/5)=1

6x=4

x=4/6=2/3

So Option B also correct.