Question

solve the system by substitution method.\

$$\begin{cases} 12x - 8y = 16 \\\\ 2y = 3x - 4 \\end{cases}$$

\
select one:\
\bigcirc a. \\ ((-2,2)\
\bigcirc b. \\ infinite solutions.\
\bigcirc c. \\ (2,2)\
\bigcirc d. \\ no solution.

Explanation:

Step1: Simplify first equation

Divide the first equation by 4:
$$\frac{12x}{4} - \frac{8y}{4} = \frac{16}{4}$$
$$3x - 2y = 4$$
Rearrange to isolate terms:
$$-2y = -3x + 4$$
$$2y = 3x - 4$$

Step2: Compare with second equation

The simplified first equation is identical to the second given equation: $2y = 3x - 4$. This means the two equations represent the same line, so every point on the line is a solution.

Answer:

B. Infinite Solutions.