Which systems of equations have infinite solutions 2x+5y=31 6x-y=13 or 2x+y=10 -6x=3y+7 or y=14-2x 6x+3y=42 or y=13-2x 4x-3y=-19 or 2x+y=14 x=13-2y or 2x+y=17 -6x=3y-51

Step-by-step explanation:

Dependent equations will have infinite solutions. One way to tell if a system of equations is dependent is to put all of the equations into standard form. Here, we can use the form ...

  ax + by = c

where a, b, c are mutually prime integers and "a" is positive. When dependent equations are put in this form, they resolve to the same equation.

Here, the rearrangement is accomplished by putting the x- and y-terms on the same side of the equal sign, with the x-term having a positive coefficient. If necessary, the constant is put on the other side, and any common factors removed from all of them.

Then the sets of equations are ...

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The 3rd and 5th sets of equations are dependent, so have infinite solutions.

The second set of equations is inconsistent, so has no solutions.

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step-by-step explanation:

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