Multiple choice

Solve the following equations for $(x,y)$. $\dfrac {2x + y}{3x - y} - \dfrac {x - y}{x + y} = 2\dfrac {8}{15}$, $7x + 5y = 29$

  1. $(1,2)$
  2. $(2,3)$
  3. $(-2,3)$
  4. $(4,2)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Testing (2,3): 7(2) + 5(3) = 14 + 15 = 29. First equation: (2*2+3)/(3*2-3) - (2-3)/(2+3) = 7/3 - (-1/5) = 7/3 + 1/5 = 35/15 + 3/15 = 38/15 = 2 8/15. Both equations are satisfied.

AI explanation

To solve the system, test the provided coordinate pairs in both equations to apply the elimination of incorrect choices. Testing the second equation with the pair (2, 3) gives 7(2) + 5(3) equals 29, which is a true statement. For the first equation with x equals 2 and y equals 3, the left side becomes (4 + 3)/(6 - 3) minus (2 - 3)/(2 + 3), which is 7/3 minus (-1/5), or 35/15 plus 3/15. This equals 38/15, which matches the right side of 2 and 8/15 (or 38/15), confirming the solution is (2, 3).

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