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6x+2y=266x+2y=-26 x6y=21x-6y=21

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Q. 6x+2y=266x+2y=-26 x6y=21x-6y=21
  1. Identify Equations: Identify the system of equations to solve.\newlineWe have two equations:\newline11) 6x+2y=266x + 2y = -26\newline22) x6y=21x - 6y = 21\newlineWe need to find the values of xx and yy that satisfy both equations simultaneously.
  2. Choose Solution Method: Choose a method to solve the system of equations.\newlineWe can use either substitution or elimination. For this problem, we will use the elimination method because it allows us to eliminate one variable by adding or subtracting the equations.
  3. Multiply Second Equation: Multiply the second equation by 22 to make the coefficients of yy in both equations equal in magnitude but opposite in sign.\newline2×(x6y)=2×212 \times (x - 6y) = 2 \times 21\newlineThis gives us a new equation:\newline2x12y=422x - 12y = 42
  4. Add Equations to Eliminate y: Add the new equation from Step 33 to the first equation to eliminate y.\newline(6x+2y)+(2x12y)=26+42(6x + 2y) + (2x - 12y) = -26 + 42\newlineThis simplifies to:\newline8x10y+2y12y=168x - 10y + 2y - 12y = 16\newline8x10y=168x - 10y = 16