Select the correct answer. Which statement best describes the solution to this system of equations? 3x + y = 17 x + 2y = 49 A. It has no solution. B. It has infinite solutions. C. It has a single solution: x = 15, y = 17. D. It has a single solution: x = -3, y = 26.

 D

Step-by-step explanation:

3x + y = 17  

x + 2y = 49    

The first thing you can do to decide the solutions they have , is by converting the equations into slope intercept forms.

3x  + y = 17      Subtract 3x from both sides

-3x           -3x

  y = -3x + 17

x + 2y = 49      Subtract x from both sides

-x              -x

  2y = -x + 49      Divide both sides by 2

 y = -1/2x + 49/2        

Compare the two equations

  y = -3x + 17

y = -1/2x +49/2

Since both equations have different slopes and different y intercepts, then the  y will have one solution .  

Use the substitution method  to solve for x by setting both equations equal each other and solve for x.

-3x + 17 = -1/2x + 49/2    Add 1/2x to both sides

+1/2x        +1/2x

 -2.5x + 17 = 24.5   Now subtract 17 from both sides

            -17      -17

   -2.5x = 7.5       Divide both sides by -2.5

x = -3

Now since we know the value of x , input it into one of the equations to solve for  y.

y = -3x + 17

y = -3(-3) + 17

y = 9 + 17

 y = 26    

This means it has only one solution and the solution is  (-3,26)

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step-by-step explanation: