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Ahmed Taha Elimination (Level 3) Mar 01, 6:55:21 PM Watch help video Solve the system of equations using elimination: 7x-6y=-2 and 2x-7y=10. Submit Answer

User Matin H
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Final answer:

To solve the system using elimination, we first make the coefficients of y the same and then eliminate y by subtracting one equation from the other, resulting in y = -2. We then substitute y = -2 back into one of the original equations to find x = -2.

Step-by-step explanation:

To solve the system of equations using elimination, we must first make the coefficients of either x or y the same in both equations. For instance, we can multiply the first equation by 2 and the second equation by 7 to make the coefficients of y the same:

  • (7x - 6y = -2) × 2 → 14x - 12y = -4
  • (2x - 7y = 10) × 7 → 14x - 49y = 70

Next, we eliminate terms by subtracting the second new equation from the first new equation:

  • 14x - 12y - (14x - 49y) = -4 - 70
  • 14x - 12y - 14x + 49y = -74
  • 37y = -74
  • y = -74 / 37
  • y = -2

Now, substitute y = -2 into one of the original equations to solve for x:

  • 7x - 6(-2) = -2
  • 7x + 12 = -2
  • 7x = -14
  • x = -2

The solution to the system of equations is x = -2 and y = -2. Finally, we check the answer to see if it is reasonable by plugging the values of x and y back into the original equations.

User Ascandroli
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