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 4.\\(\\ \\)the result after completing the multiplication is 4.\\(\\ \\)(type an equation. type your answer in standard form.)

Explanation:

Step1: Determine multiplier for y - elimination

The first equation has \(4y\), the second has \(-y\). To eliminate \(y\), multiply the second equation by \(4\) (so \(-y\times4=-4y\), and \(4y + (-4y)=0\)).

Step2: Multiply second equation by 4

Take the second equation \(2x - y=-12\). Multiply each term by \(4\):
\(4\times(2x) - 4\times(y)=4\times(-12)\)
Simplify: \(8x - 4y=-48\)

Answer:

To eliminate \(y\), multiply the second equation by \(4\). The result is \(8x - 4y=-48\).