of linear combination, the solution set of the system $$ \left\{\begin{array}{l}3(2 x-3 y)=-2 \ 5-15 y=-10 x\end{array} ight. $$

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of linear combination, the solution set of the system $$ \left\{\begin{array}{l}3(2 x-3 y)=-2 \ 5-15 y=-10 x\end{array}ight. $$

UpStudy AI · Accepted Answer

To find the solution set of the system of linear equations, we need to solve the system of equations.

Given system of equations:
$$ \left\{\begin{array}{l}3(2 x-3 y)=-2 \ 5-15 y=-10 x\end{array}\right. $$

Let's solve the system of equations step by step.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}3\left(2x-3y\right)=-2\5-15y=-10x\end{array}\right.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}3\left(2x-3y\right)=-2\x=\frac{-1+3y}{2}\end{array}\right.$$
- step2: Substitute the value of $$x:$$
  $$3\left(2\times \frac{-1+3y}{2}-3y\right)=-2$$
- step3: Simplify:
  $$-3=-2$$
- step4: Calculate:
  $$\left\{ \begin{array}{l}x \in \varnothing \y \in \varnothing \end{array}\right.$$
- step5: Rewrite:
  $$(x, y) \in \varnothing$$
The solution set of the system of linear equations is empty, which means there is no solution to the system of equations.
There is no solution to the system of equations.

of linear combination, the solution set of the system \( \left\{\begin{array}{l}3(2 x-3 y)=-2 \\ 5-15 y=-10 x\end{array}\right. \)

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