Question

tomass equation
tomas wrote the equation $y = 3x + \frac{3}{4}$. when sandra wrote her equation, they discovered that her equation had all the same solutions as tomass equation. which equation could be sandras?
\\(\boldsymbol{-6x + y = \frac{3}{2}}\\)
\\(\boldsymbol{6x + y = \frac{3}{2}}\\)
\\(\boldsymbol{-6x + 2y = \frac{3}{2}}\\)
\\(\boldsymbol{6x + 2y = \frac{3}{2}}\\)

Explanation:

Step1: Recall equivalent equations rule

Equations are equivalent if one can be transformed into the other by multiplying/dividing all terms by a non-zero constant.

Step2: Multiply Tomas's equation by 2

Start with $y = 3x + \frac{3}{4}$. Multiply every term by 2:
$$2y = 6x + \frac{3}{2}$$

Step3: Rearrange to match options

Rearrange the equation to isolate the constant term on the right:
$$-6x + 2y = \frac{3}{2}$$

Step4: Match with given options

Compare the derived equation to the choices.

Answer:

$\boldsymbol{-6x + 2y = \frac{3}{2}}$ (third option)