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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.

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4 votes

Answer: D

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)

User Francis Nepomuceno
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