Why does adding a multiple of one equation to another keep the same solution?

The step is reversible, so the solution set is unchanged

For the inequality $y > x - 2$, the boundary line is:

Dashed, because the inequality is strict

The solution is non-viable in context

12questions. Pick an answer and you'll see why right away.

Solve the system $y = x + 4$ and $2x + y = 13$ .
Solve the system $2x + y = 10$ and $2x - y = 2$ .
Which method is most efficient for $y = 3x - 1$ and $x + 2y = 12$ ?
At what point do $y = x + 2$ and $y = -2x + 8$ intersect?
Two distinct lines have the same slope. How many solutions does the system have?
Why does adding a multiple of one equation to another keep the same solution?
For the inequality $y > x - 2$ , the boundary line is:
For $2x + y \le 6$ , is $(0, 0)$ in the solution region?
Adult tickets cost $\$ 9 $and child tickets cost$ \ $4$ . A family buys $6$ tickets for $\$ 39$. How many adult tickets?
A system that models people at an event gives $x = -4$ . What is the correct conclusion?
A system simplifies to $0 = 0$ after eliminating both variables. How many solutions?
Which system has no solution?