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What is the solution to the system of equations 10x + 16y = 6 and 5x - 8y = 5?

User Xbalaj
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Final answer:

The solution to the system of equations is x = 0.8 and y = -0.125, found through the elimination method by multiplying the second equation by 2 and then adding to the first to eliminate y.

Step-by-step explanation:

The solution to the system of equations 10x + 16y = 6 and 5x - 8y = 5 can be found using either substitution or elimination methods. To use elimination, we can multiply the second equation by 2 to make the coefficients of y in both equations equal with opposite signs:

  • 10x + 16y = 6
  • (5x - 8y = 5) * 2 ⇒ 10x - 16y = 10

Add the two equations to eliminate y:

  1. 10x + 16y + 10x - 16y = 6 + 10
  2. 20x = 16
  3. x = 16 / 20
  4. x = 0.8

Now substitute x = 0.8 into the first equation to solve for y:

  1. 10(0.8) + 16y = 6
  2. 8 + 16y = 6
  3. 16y = 6 - 8
  4. 16y = -2
  5. y = -2 / 16
  6. y = -0.125

The solution to the system of equations is x = 0.8 and y = -0.125.

User Gary Brunton
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