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

ANSWER

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

Answer 2

Answer:

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

Step-by-step 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.