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?\

$$\begin{cases}5x + 3y = -8\\\\2x - y = -13\\end{cases}$$

\to eliminate the variable y, multiply the second equation by 3.\the result after completing the multiplication is \square.\\(type an equation. type your answer in standard form.)

Explanation:

Step1: Identify the second equation

The second equation is \(2x - y = -13\).

Step2: Multiply the second equation by 3

Multiply each term in \(2x - y = -13\) by 3.
For the \(x\)-term: \(3\times2x = 6x\)
For the \(y\)-term: \(3\times(-y)= - 3y\)
For the constant term: \(3\times(-13)=-39\)
So the resulting equation is \(6x - 3y=-39\)

Answer:

\(6x - 3y = - 39\)