Question

1. solve the following system of linear equations by elimination.

\

$$\begin{cases} 2x - 5y = 1 \\\\ -3x + 2y = -18 \\end{cases}$$

what is the value of y?
\bigcirc \\ y = -3
\bigcirc \\ y = 3
\bigcirc \\ y = -1.5
\bigcirc \\ y = 1.5

Explanation:

Step1: Multiply equations to eliminate x

Multiply the first equation \(2x - 5y = 1\) by 3: \(3(2x - 5y)=3(1)\) → \(6x - 15y = 3\).
Multiply the second equation \(-3x + 2y = -18\) by 2: \(2(-3x + 2y)=2(-18)\) → \(-6x + 4y = -36\).

Step2: Add the two new equations

Add \(6x - 15y = 3\) and \(-6x + 4y = -36\):
\((6x - 6x)+(-15y + 4y)=3 + (-36)\) → \(-11y = -33\).

Step3: Solve for y

Divide both sides by \(-11\): \(y=\frac{-33}{-11}=3\).

Answer:

\(y = 3\) (Option: \(y = 3\))