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Solve the system of equations. {:[14 x+5y=31],[2x-3y=-29],[x=◻],[y=◻]:}

Solve the system of equations.\newline14x+5y=312x−3y=−29x=□y=□ \begin{array}{l} 14 x+5 y=31 \\ 2 x-3 y=-29 \\ x=\square \\ y=\square \end{array}

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Q. Solve the system of equations.\newline14x+5y=312x−3y=−29x=□y=□ \begin{array}{l} 14 x+5 y=31 \\ 2 x-3 y=-29 \\ x=\square \\ y=\square \end{array}
  1. Multiply second equation by 77: Multiply the second equation by 77 to make the coefficient of xx in both equations the same.\newlineCalculation: 7×(2x−3y)=7×(−29)7 \times (2x - 3y) = 7 \times (-29)\newline14x−21y=−20314x - 21y = -203
  2. Subtract new equation from first equation: Subtract the new equation from the first equation to eliminate xx.\newlineCalculation: (14x+5y)−(14x−21y)=31−(−203)(14x + 5y) - (14x - 21y) = 31 - (-203)\newline14x+5y−14x+21y=31+20314x + 5y - 14x + 21y = 31 + 203\newline26y=23426y = 234
  3. Solve for y: Solve for y by dividing both sides of the equation by 2626.\newlineCalculation: 26y26=23426\frac{26y}{26} = \frac{234}{26}\newliney = 99
  4. Substitute y=9y = 9 into first equation: Substitute y=9y = 9 into the first original equation to solve for xx.\newlineCalculation: 14x+5(9)=3114x + 5(9) = 31\newline14x+45=3114x + 45 = 31\newline14x=31−4514x = 31 - 45\newline14x=−1414x = -14
  5. Solve for x: Solve for x by dividing both sides of the equation by 1414.\newlineCalculation: 14x14=−1414 \frac{14x}{14} = \frac{-14}{14} \newlinex=−1 x = -1

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