Multiple choice

Solve the following pair of simultaneous equations: $5x\, -\, 6y\, =\, 8$ $7y\, -\, 15x\,=\, 9$

  1. (1 , 3)

  2. (6 , -1)

  3. (-2 , -3)

  4. (3 , -5)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Substitute the values from option C into the equations. For 5x - 6y = 8, 5(-2) - 6(-3) = -10 + 18 = 8. For 7y - 15x = 9, 7(-3) - 15(-2) = -21 + 30 = 9. Both equations are satisfied.

AI explanation

Rearrange the second equation to isolate y, giving 7y = 15x + 9 and y = (15x + 9)/7. Substitute this expression for y into the first equation to get 5x - 6((15x + 9)/7) = 8. Multiplying by 7 to clear the denominator gives 35x - 90x - 54 = 56. Solving -55x = 110 gives x = -2. Substituting x = -2 into y = (15x + 9)/7 yields y = (-30 + 9)/7 = -3, so the solution is (-2, -3).

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