$$ \left.\begin{array}{|l|l|}\hline ext { 4. } x-y=2 & \ \hline ext {-int: } \ \hline ext { 5. } 3 x-2 y=12 & \ & \ \hline ext { 6. } 8 x+10 y=-10 & y ext {-int: } \ \hline\end{array} ight] $$

Question

$$ \left.\begin{array}{|l|l|}\hline 	ext { 4. } x-y=2 & \ \hline 	ext {-int: } \ \hline 	ext { 5. } 3 x-2 y=12 & \ & \ \hline 	ext { 6. } 8 x+10 y=-10 & y 	ext {-int: } \ \hline\end{array}ight] $$

UpStudy AI · Accepted Answer

We have a system of equations to solve:

1. $$ x - y = 2 $$
2. $$ 3x - 2y = 12 $$
3. $$ 8x + 10y = -10 $$

Let's solve these equations together.

I will set up the equations in standard LaTeX format for the tool call:

1. $$ x - y = 2 $$
2. $$ 3x - 2y = 12 $$
3. $$ 8x + 10y = -10 $$

Now, I will proceed to solve this system of equations.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}x-y=2\3x-2y=12\8x+10y=-10\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=2+y\3x-2y=12\8x+10y=-10\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$\left\{ \begin{array}{l}3\left(2+yight)-2y=12\8\left(2+yight)+10y=-10\end{array}ight.$$
- step3: Simplify:
  $$\left\{ \begin{array}{l}6+y=12\16+18y=-10\end{array}ight.$$
- step4: Solve the equation:
  $$\left\{ \begin{array}{l}y=6\16+18y=-10\end{array}ight.$$
- step5: Substitute the value of $$y:$$
  $$16+18	imes 6=-10$$
- step6: Simplify:
  $$124=-10$$
- step7: Calculate:
  $$\left\{ \begin{array}{l}x \in \varnothing \y \in \varnothing \end{array}ight.$$
- step8: Rewrite:
  $$(x, y) \in \varnothing$$
The result of solving the system of equations is that there is no solution. This means that the equations are inconsistent and do not intersect at any point.
There is no solution to the system of equations.

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