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What is the solution to the following pair of simultaneous equations?𝑦=2𝑥+12𝑦−𝑥=−1y=2x+12y−x=−1

Question

What is the solution to the following pair of simultaneous equations?

y=2x+12 y = 2x + 12

y−x=−1 y - x = -1

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Solution

The pair of simultaneous equations given are:

  1. y = 2x + 1
  2. y - x = -1

Let's solve them step by step:

Step 1: From equation 2), we can express x in terms of y: x = y + 1

Step 2: Substitute x from step 1) into equation 1): y = 2(y + 1) + 1

Step 3: Simplify the equation: y = 2y + 2 + 1

Step 4: Rearrange the equation to find y: -y = 3, so y = -3

Step 5: Substitute y = -3 into equation 2) to find x: -3 - x = -1, so x = -2

So, the solution to the pair of simultaneous equations is x = -2 and y = -3.

This problem has been solved

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