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{:[3x+2y=8],[2x-y=3]:} What is the solution (x,y) to the given system of equations? A) (3,2) B) (2,3) C) (1,2) D) (2,1)

3x+2y=82x−y=3 \begin{array}{c} 3 x+2 y=8 \\ 2 x-y=3 \end{array} \newlineWhat is the solution (x,y) (x, y) to the given system of equations?\newlineA) (3,2) (3,2) \newlineB) (2,3) (2,3) \newlineC) (1,2) (1,2) \newlineD) (2,1) (2,1)

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Full solution

Q. 3x+2y=82x−y=3 \begin{array}{c} 3 x+2 y=8 \\ 2 x-y=3 \end{array} \newlineWhat is the solution (x,y) (x, y) to the given system of equations?\newlineA) (3,2) (3,2) \newlineB) (2,3) (2,3) \newlineC) (1,2) (1,2) \newlineD) (2,1) (2,1)
  1. Write Equations: Step 11: Write down the system of equations.\newline\begin{cases}3x+2y=8\2x-y=3\end{cases}
  2. Solve for yy: Step 22: Solve for yy from the second equation.y=2x−3y = 2x - 3
  3. Substitute and Simplify: Step 33: Substitute yy in the first equation.3x+2(2x−3)=83x + 2(2x - 3) = 83x+4x−6=83x + 4x - 6 = 87x−6=87x - 6 = 8
  4. Solve for x: Step 44: Solve for x.\newline7x=147x = 14\newlinex=2x = 2
  5. Substitute xx for yy: Step 55: Substitute xx back into the equation for yy.y=2(2)−3y = 2(2) - 3y=4−3y = 4 - 3y=1y = 1

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