Question

Select the correct answer.
Which statement best describes the solution to this system of equations?
3x + y= 17
x+2y= 49
OA. It has no solution.
OB.
It has infinite solutions.
OC. It has a single solution: x= 15, y= 17.
OD. It has a single solution: x= -3, y = 26.
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Answer 1

Answer:

  D. (-3, 26)

Step-by-step explanation:

The ratios of x- and y-coefficients are different in the two equations, so there will be a single solution. (Different ratios mean the slopes are different. Lines with different slopes must intersect in exactly one point.)

We can rearrange the first equation to give an expression for y:

  y = 17 -3x

This can be substituted into the second equation to give ...

  x +2(17 -3x) = 49

  -5x +34 = 49 . . . . . . simplify

  -5x = 15 . . . . . . . subtract 34

  x = -3 . . . . . . divide by -5

Then the value of y is ...

  y = 17 -3(-3) = 26

The single solution is (x, y) = (-3, 26).