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Find the solution of the system of equations. {:[-4x-2y=-30],[-4x-7y=-25](_________,________)":}

Find the solution of the system of equations.\newline−4x−2y=−30−4x−7y=−25 \begin{array}{l} -4 x-2 y=-30 \\ -4 x-7 y=-25 \end{array} \newline(_________,________)

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Full solution

Q. Find the solution of the system of equations.\newline−4x−2y=−30−4x−7y=−25 \begin{array}{l} -4 x-2 y=-30 \\ -4 x-7 y=-25 \end{array} \newline(_________,________)
  1. Label Equations: First, let's label the equations for reference:\newlineEquation 11: −4x−2y=−30-4x - 2y = -30\newlineEquation 22: −4x−7y=−25-4x - 7y = -25
  2. Eliminate x: Subtract Equation 22 from Equation 11 to eliminate x: (−4x−2y)−(−4x−7y)=−30−(−25)(-4x - 2y) - (-4x - 7y) = -30 - (-25)
  3. Simplify Subtraction: Simplify the subtraction: −4x+4x−2y+7y=−30+25-4x + 4x - 2y + 7y = -30 + 25
  4. Combine Like Terms: Combine like terms: 0x+5y=−50x + 5y = -5
  5. Solve for y: Solve for y:\newline5y=−55y = -5\newliney=−55y = \frac{-5}{5}\newliney=−1y = -1
  6. Substitute yy into Equation: Now substitute y=−1y = -1 into Equation 11 to find xx:−4x−2(−1)=−30-4x - 2(-1) = -30
  7. Simplify Equation: Simplify the equation: −4x+2=−30-4x + 2 = -30
  8. Subtract from Both Sides: Subtract 22 from both sides:\newline−4x=−32-4x = -32
  9. Divide to Solve for x: Divide by −4-4 to solve for x:\newlinex=−32−4x = \frac{-32}{-4}\newlinex=8x = 8

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