Question

In the system of equations below, I want to eliminate the variable y.

3x + 5y = 2
6x - 10y = -16
The first step to solving this system of equations is multiplying the first equation
by a number other than -1. Which number would that be?
The answer choices are..
-2
5
-5
2
0 -5
2.

Answer 1

(x,y)=(-1,1)

Explanation:

Given that,

3x + 5y = 2 .....(1)

6x - 10y = -16 ....(2)

Finding the value of x from equation (1).

`x=(2-5y)/(3)`

Put the value of x in equation (2)

`6((2-5y)/(3)) - 10y = -16\\\\2(2-5y)-10y=-16\\\\4-10y-10y=-16\\\\-20y=-16-4\\\\y=1`

Put the value of y in equation (1) :

`3x + 5(1) = 2\\\\3x=2-5\\\\3x=-3\\\\x=-1`

So, the solution of the equations is (-1,1).