Question

4a. by what number should the top equation by multiplied by so that when the equations are combined, the xs are eliminated?
\

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

\bigcirc 3
\bigcirc -3
\bigcirc -2
\bigcirc -6
\bigcirc 6
\bigcirc 2

Explanation:

Step1: Identify x coefficients

Top equation: $-x$ (coefficient: $-1$); Bottom equation: $2x$ (coefficient: $2$)

Step2: Find multiplier for x elimination

Let multiplier be $k$. We need $k\times(-1) + 2 = 0$.
Solve for $k$:
$$k\times(-1) = -2$$
$$k = 2$$
Verify: Multiply top equation by 2: $2(-x+3y)=2(-3) \implies -2x+6y=-6$. Add to bottom equation: $(-2x+6y)+(2x-6y)=-6+6 \implies 0=0$, x is eliminated.

Answer:

2