Answer:
- y=14-2x; 6x+3y=42
- 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 ...
- 2x +5y = 31
- 6x -y = 13 . . . . not dependent
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- 2x +y = 10
- 6x +3y = -7 . . . . not dependent
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- 2x +y = 14
- 2x +y = 14 . . . . dependent
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- 2x +y = 13
- 4x -3y = -19 . . . . not dependent
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- 2x +y = 14
- x +2y = 13 . . . . not dependent
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- 2x +y = 17
- 2x +y = 17 . . . . dependent
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The 3rd and 5th sets of equations are dependent, so have infinite solutions.
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The second set of equations is inconsistent, so has no solutions.
