Question

match each system to the number the first equation can be multiplied by to eliminate the x - terms when adding to the second equation.
10x - 4y=-8
-5x + 6y = 10
3x - 8y = 1
6x + 5y = 12
-8x + 10y = 16
-4x - 5y = 13
-2x + 6y = 3
4x + 3y = 9

Explanation:

Step1: Analyze first - system

For the system

$$\begin{cases}10x - 4y=-8\\-5x + 6y = 10\end{cases}$$

, to eliminate $x$ when adding the two equations, if we multiply the second - equation by 2, the coefficient of $x$ in the second equation becomes $- 10$. So we multiply the first equation by $\frac{1}{2}$. The coefficient of $x$ in the first equation will be $5$ and when added to the second equation ($-5x$), $x$ will be eliminated.

Step2: Analyze second - system

For the system

$$\begin{cases}3x-8y = 1\\6x + 5y=12\end{cases}$$

, if we want to eliminate $x$, we note that the coefficient of $x$ in the second equation is $6$. If we multiply the first equation by $- 2$, the coefficient of $x$ in the first equation becomes $-6$. Then when added to the second equation, $x$ will be eliminated.

Step3: Analyze third - system

For the system

$$\begin{cases}-8x + 10y=16\\-4x-5y = 13\end{cases}$$

, if we multiply the second equation by 2, the coefficient of $x$ in the second equation becomes $-8$. To eliminate $x$, we multiply the first equation by $-\frac{1}{2}$. The coefficient of $x$ in the first equation will be $4$ and when added to the second equation ($-4x$), $x$ will be eliminated.

Step4: Analyze fourth - system

For the system

$$\begin{cases}-2x + 6y=3\\4x+3y = 9\end{cases}$$

, to eliminate $x$, we multiply the first equation by 2. The coefficient of $x$ in the first equation becomes $-4$. Then when added to the second equation ($4x$), $x$ will be eliminated.

Answer:

1. $\frac{1}{2}$
2. $-2$
3. $-\frac{1}{2}$
4. $2$