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What is the result of adding these two equations? {:[2x+7y=4],[-2x-8y=-2]:}

What is the result of adding these two equations?\newline2x+7y=4−2x−8y=−2 \begin{array}{c} 2 x+7 y=4 \\ -2 x-8 y=-2 \end{array}

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Full solution

Q. What is the result of adding these two equations?\newline2x+7y=4−2x−8y=−2 \begin{array}{c} 2 x+7 y=4 \\ -2 x-8 y=-2 \end{array}
  1. Identify operation to combine: Identify the operation to combine the equations. We will add the two equations to eliminate the variable 'xx'.
  2. Add equations to eliminate x: Add the equations (2x+7y)+(−2x−8y)=4+(−2)(2x + 7y) + (-2x - 8y) = 4 + (-2).
  3. Combine like terms: Combine like terms. 2x−2x+7y−8y=4−22x - 2x + 7y - 8y = 4 - 2.
  4. Simplify the equation: Simplify the equation. The xx terms cancel out, and we are left with −1y=2-1y = 2.
  5. Solve for y: Solve for 'y'. Dividing both sides of the equation by −1-1 gives us y=−2y = -2.

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