Question

solve the system of equations by the substitution method.\

$$\begin{cases}3x - y = 2\\\\5x - 2y = 6\\end{cases}$$

\
select the correct choice below and, if necessary, fill in the answer box to complete your choice.\
\bigcirc a. the solution is \square. (simplify your answer. type an ordered pair.)\
\bigcirc b. there are infinitely many solutions.\
\bigcirc c. there is no solution.

Explanation:

Step1: Solve first equation for y

From \(3x - y = 2\), we can rearrange to get \(y = 3x - 2\).

Step2: Substitute y into second equation

Substitute \(y = 3x - 2\) into \(5x - 2y = 6\). So we have \(5x - 2(3x - 2) = 6\).

Step3: Simplify and solve for x

Expand the equation: \(5x - 6x + 4 = 6\). Combine like terms: \(-x + 4 = 6\). Subtract 4 from both sides: \(-x = 2\), so \(x = -2\).

Step4: Find y using x

Substitute \(x = -2\) into \(y = 3x - 2\). Then \(y = 3(-2) - 2 = -6 - 2 = -8\).

Answer:

A. The solution is \((-2, -8)\)