Question

Y + 3x = -4

2x - 3y = -21
Which equivalent equation could Vito use?

A. 2(-3x – 4) + 3x = -21
B. 2(3x – 4) + 3x = -21
C. 2x - 3(-3x – 4) = -21
D. 2x - 3(3x - 4) = -21

Answer 1

Vito could use the equivalent equation 2x - 3(-3x - 4) = -21 to represent the system of equations.

Step-by-step explanation:

The equivalent equation that Vito could use is option C. 2x - 3(-3x - 4) = -21.

To determine the equivalent equation, we need to manipulate the given system of equations in a way that isolates y in terms of x. Let's start with the first equation:

y + 3x = -42

Subtracting 3x from both sides, we get:

y = -3x - 42

Now let's move on to the second equation:

-42x - 3y = -21

Adding 42x to both sides, we get:

-3y = 42x - 21

Dividing both sides by -3, we get:

y = -14x + 7

So the equivalent equation is y = -14x + 7.

To check which option matches this equation, let's simplify each option and compare it to y = -14x + 7. Option C simplifies to 2x - 9x + 12 = -21, which can be further simplified to -7x + 12 = -21. Therefore, the equivalent equation that Vito could use is option C.