Question

to solve the following system by the addition method and eliminate the variable y, by what value should the second equation be multiplied? what will be the result after completing the multiplication? \

$$\begin{cases} 5x + 4y = -6 \\\\ 2x - y = -12 \\end{cases}$$

to eliminate the variable y, multiply the second equation by \square

Explanation:

Step1: Analyze y - coefficients

First equation: \(5x + 4y=-6\) (y - coefficient is \(4\))
Second equation: \(2x - y=-12\) (y - coefficient is \(- 1\))
To eliminate \(y\), we need the coefficients of \(y\) to be opposites (or equal in magnitude and opposite in sign) when added. So we multiply the second equation by \(4\) (since \(4\times(- 1)=-4\), and \(4+(-4) = 0\) when we add the equations).

Step2: Verify the multiplication

Multiply each term in \(2x - y=-12\) by \(4\):
\(4\times(2x)-4\times(y)=4\times(-12)\)
\(8x-4y = - 48\)

Answer:

To eliminate the variable \(y\), multiply the second equation by \(\boldsymbol{4}\). The result after multiplication is \(8x - 4y=-48\). (For the first blank in the problem, the answer is \(4\))