Question

4) Which step could be completed in order to prepare the system of equations below for the elimination method?

1st equation: 5x-3y=10

2nd equation: 8x+6y=15


A) Multiply the 1st equation by -2

B)Multiply the 2nd equation by 2

C)Multiply the 1st equation by 2

D)Multiply the 2nd equation by -2

Answer 1

Option C - Multiply the 1st equation by 2

Explanation:

To find : Which step could be completed in order to prepare the system of equations below for the elimination method?

Solution :

1st equation:
`5x-3y=10`

2nd equation:
`8x+6y=15`

For elimination method,

We eliminate the y by multiplying 1st equation by 2 and add by 2nd equation.

i.e. 1st equation became
`10x-6y=20`

Add with 2nd equation,

`10x-6y+8x+6y=20+15`

`18x=35`

`x=(35)/(18)`

Substitute in (1),

`5((35)/(18))-3y=10`

`(175)/(18)-3y=10`

`3y=(175)/(18)-10`

`3y=(175-180)/(18)`

`3y=(-5)/(18)`

`y=(-5)/(54)`

Therefore, the step could be completed in order to prepare the system of equations below for the elimination method is option C.