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(iii) {:[3x+7y=27],[5x+2y=16]:}

(iii) 3x+7y=275x+2y=16 \begin{array}{r}3 x+7 y=27 \\ 5 x+2 y=16\end{array}

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Full solution

Q. (iii) 3x+7y=275x+2y=16 \begin{array}{r}3 x+7 y=27 \\ 5 x+2 y=16\end{array}
  1. Multiply Equations by Constants: Multiply the first equation by 22 and the second equation by 77 to eliminate yy.2(3x+7y)=2(27)2(3x + 7y) = 2(27)7(5x+2y)=7(16)7(5x + 2y) = 7(16)
  2. Perform Multiplication: Perform the multiplication.\newline6x+14y=546x + 14y = 54\newline35x+14y=11235x + 14y = 112
  3. Subtract Equations: Subtract the first new equation from the second new equation to eliminate yy.(35x+14y)−(6x+14y)=112−54(35x + 14y) - (6x + 14y) = 112 - 54
  4. Simplify Equation: Simplify the equation. 29x=5829x = 58
  5. Divide to Solve for xx: Divide both sides by 2929 to solve for xx.x=5829x = \frac{58}{29}
  6. Calculate x Value: Calculate the value of x.\newlinex=2x = 2
  7. Substitute xx into Equation: Substitute x=2x = 2 into the original first equation to solve for yy.3(2)+7y=273(2) + 7y = 27
  8. Simplify Equation: Simplify the equation. 6+7y=276 + 7y = 27
  9. Calculate yy Value: Subtract 66 from both sides.\newline7y=27−67y = 27 - 6
  10. Solve for y: Calculate the value of y.\newline7y=217y = 21\newliney=217y = \frac{21}{7}
  11. Solve for y: Calculate the value of y.\newline7y=217y = 21\newliney=217y = \frac{21}{7}Solve for y.\newliney=3y = 3

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