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Solve the system of equations. {:[10 x-3y-81=0],[-5x-7y-19=0],[x=◻],[y=◻]:}

Solve the system of equations.\newline10x−3y−81=0−5x−7y−19=0x=□y=□ \begin{array}{l} 10 x-3 y-81=0 \\ -5 x-7 y-19=0 \\ x=\square \\ y=\square \end{array}

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Q. Solve the system of equations.\newline10x−3y−81=0−5x−7y−19=0x=□y=□ \begin{array}{l} 10 x-3 y-81=0 \\ -5 x-7 y-19=0 \\ x=\square \\ y=\square \end{array}
  1. Multiply second equation by 22: Multiply the second equation by 22 to prepare for elimination of x.\newlineCalculation: 2×(−5x−7y=19)→−10x−14y=382 \times (-5x - 7y = 19) \rightarrow -10x - 14y = 38
  2. Add modified second equation to first equation: Add the modified second equation to the first equation to eliminate xx.\newline Calculation: (10x−3y=81)+(−10x−14y=38)→−17y=119(10x - 3y = 81) + (-10x - 14y = 38) \rightarrow -17y = 119
  3. Solve for y: Solve for y.\newlineCalculation: −17y=119→y=119−17→y=−7-17y = 119 \rightarrow y = \frac{119}{-17} \rightarrow y = -7
  4. Substitute y=−7y = -7 into first equation: Substitute y=−7y = -7 into the first original equation to solve for xx.\newlineCalculation: 10x−3(−7)=81→10x+21=81→10x=81−21→10x=60→x=6010→x=610x - 3(-7) = 81 \rightarrow 10x + 21 = 81 \rightarrow 10x = 81 - 21 \rightarrow 10x = 60 \rightarrow x = \frac{60}{10} \rightarrow x = 6
  5. Write solution as coordinate point: Write the solution as a coordinate point.\newlineThe solution is (6,−7)(6, -7).

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