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−4x−8y=−20;8x+3y=1-4x-8y=-20; 8x+3y=1

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Q. −4x−8y=−20;8x+3y=1-4x-8y=-20; 8x+3y=1
  1. Write Equations: Write down the system of equations to analyze the problem.\newline−4x−8y=−20-4x - 8y = -20\newline8x+3y=18x + 3y = 1
  2. Elimination Method: Attempt to solve the system of equations using the elimination method. To do this, we can multiply the second equation by 44 to make the coefficient of xx in both equations the same.\newline4×(8x+3y)=4×14 \times (8x + 3y) = 4 \times 1\newlineThis gives us:\newline32x+12y=432x + 12y = 4
  3. New System: Now we have the new system of equations:\newline−4x−8y=−20-4x - 8y = -20\newline32x+12y=432x + 12y = 4\newlineWe can add these two equations together to eliminate x.\newline(−4x−8y)+(32x+12y)=−20+4(-4x - 8y) + (32x + 12y) = -20 + 4
  4. Add Equations: Perform the addition of the two equations.\newline(−4x+32x)+(−8y+12y)=−20+4(-4x + 32x) + (-8y + 12y) = -20 + 4\newline28x+4y=−1628x + 4y = -16\newlineThis is incorrect because the correct addition should be:\newline(−4x+32x)+(−8y+12y)=−20+4(-4x + 32x) + (-8y + 12y) = -20 + 4\newline28x+4y=−1628x + 4y = -16 is not the correct equation after adding the two equations together. The correct equation should be:\newline28x+4y=−1628x + 4y = -16

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