Question

question
which system of equations has the same solution as the system below?
$2x + 5y = 45$
$6x + 4y = 58$
answer
$\circ$ $-6x - 15y = 45$
$6x + 4y = 58$
$\circ$ $-6x - 15y = -135$
$6x + 4y = 58$
$\circ$ $-6x + 5y = -135$
$6x + 4y = 58$
$\circ$ $2x - 15y = -135$
$6x + 4y = 58$
submit answer

Explanation:

Step1: Recall the property of linear systems

A system of linear equations has the same solution if we multiply one of the equations by a non - zero constant. For the equation \(2x + 5y=45\), if we multiply both sides by \(- 3\), we use the property \(a = b\Rightarrow ca=cb\) (\(c
eq0\)).
Multiply \(2x + 5y = 45\) by \(-3\):
\[

$$\begin{align*} -3\times(2x + 5y)&=-3\times45\\ -6x-15y&=- 135 \end{align*}$$

\]
The second equation \(6x + 4y = 58\) remains unchanged. So the system \(

$$\begin{cases}-6x - 15y=-135\\6x + 4y = 58\end{cases}$$

\) has the same solution as the original system \(

$$\begin{cases}2x + 5y = 45\\6x + 4y = 58\end{cases}$$

\)

Answer:

\(-6x - 15y=-135\)
\(6x + 4y = 58\) (the second option among the given choices)