Answer:
Hope this helps, got it from a different website.
Explanation:
3x+y=6
3x+y=6 is the new equation that has exactly one solution in common with Elena's equation. .A equation is said to have exactly one solution with this, if the set of equations meet at a point, or have a unique point of intersection. This only happens when the coefficient of x and the coefficient of y are different in the new equation. Solving these pair of equations gives us (1,2) as a unique point.
6x+2y=8
6x+2y=8 is the new equation which has no solutions in common with Elena's equation. An equation is said to have no solutions when the coefficients of both x and y are the same but the constant is different.
6x+2y=12
6x+2y=12 is the equation that has infinitely many solutions in common with Elena's equation. An equation is said to have infinitely many solutions if the result will be 0=0.