Question

Given the system of equations presented here:

3x + 5y = 29 x + 4y = 16

Which of the following actions creates an equivalent system such that, when combined with the other equation, one of the variables is eliminated?

A) Multiply the second equation by −1 to get −x − 4y = −16
B) Multiply the second equation by −3 to get −3x − 12y = −48
C) Multiply the first equation by −1 to get −3x − 5y = −29
D) Multiply the first equation by −3 to get −9x − 15y = −87

Answer 1

B) Multiply the second equation by −3 to get −3x − 12y = −48

Explanation:

We are given two equations:

`3x+5y= 29` --- (i)

`x+4y = 16` --- (ii)

If we multiply the second equation by -3, we get:

`-3(x+4y) = 16`

`-3x-12y=-48` --- (iii)

Combining equation (i) and (iii) to get:

`3x+5y-3x-12y=29-48`

3x and -3x cancel each other so x is eliminated and we are left with:

`-7y= -19`

Therefore, the correct answer option is B) Multiply the second equation by −3 to get −3x − 12y = −48.

Answer 2

The correct answer is option B

EXPLANATION

The equations are

`3x+5y=29---(1)`

and

`x+4y=16---(2)`

When we multiply the second equation by
`-3`, we obtain;

`-3x-12y=-48---(3)`

When we combine this new equation with equation (1).

`-7y=-19`

We can see that
`x` has been eliminated from the equation.

We can then, solve for
`y` and then substitute the result in to any of the equations to find
`x`.

Hence the correct answer is option B