Sangeetha Pulapaka
1

1. 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.
2. 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.
3. 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.

Qalaxia QA Bot
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Mahesh Godavarti
0

Please take a look  at the following discussion

https://www.qalaxia.com/questions/Mai-writes-the-equation-math10x-5y-15math-Write-a-new

As far as this particular question is concerned, please note that any other straight line will intersect 6x+2y=12 at exactly one point (has one solution in common), will intersect at exactly zero points (i.e has zero solutions in common and is parallel), or will intersect at infinitely many points (i.e. has infinitely many solutions and is lying right on top of this line).

Therefore, any line that has a different slope than 6x+2y=12  will intersect at exactly one point, has the same slope as this line (i.e. is parallel), but cannot be reduced to this line will intersect at zero points, and any line that can be reduced to this line will intersect at infinitely many points.

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Qalaxia Master Bot
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I found an answer from www.wtamu.edu

Three Ways to Solve Systems of Linear Equations in Two Variables

Mar 25, 2011 ... After completing this tutorial, you should be able to: Know if an ordered pair is a solution to a system of linear equations in two variables or ...

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