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Find the solution of the system of equations.

{:[-x+6y=23],[-8x-3y=31]:}

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Find the solution of the system of equations.\newlinex+6yamp;=238x3yamp;=31 \begin{aligned} -x+6 y & =23 \\ -8 x-3 y & =31 \end{aligned} \newline(,) (\square, \square)

Full solution

Q. Find the solution of the system of equations.\newlinex+6y=238x3y=31 \begin{aligned} -x+6 y & =23 \\ -8 x-3 y & =31 \end{aligned} \newline(,) (\square, \square)
  1. Write Equations: Write down the system of equations to be solved.\newlineWe have the following system of equations:\newline11) x+6y=23-x + 6y = 23\newline22) 8x3y=31-8x - 3y = 31\newlineWe will use the method of substitution or elimination to find the values of xx and yy that satisfy both equations.
  2. Choose Solution Method: Decide which method to use for solving the system.\newlineWe can use either substitution or elimination. In this case, we will use the elimination method because it seems straightforward to eliminate xx by multiplying the first equation by 88 and adding it to the second equation.
  3. Multiply First Equation: Multiply the first equation by 88 to prepare for elimination.\newlineMultiplying the first equation by 88 gives us:\newline8(x+6y)=8(23)8(-x + 6y) = 8(23)\newlineWhich simplifies to:\newline8x+48y=184-8x + 48y = 184
  4. Add Equations for Elimination: Add the new equation to the second equation to eliminate xx. We add 8x+48y=184-8x + 48y = 184 (from Step 33) to 8x3y=31-8x - 3y = 31 (the second original equation): (8x+48y)+(8x3y)=184+31(-8x + 48y) + (-8x - 3y) = 184 + 31 This simplifies to: 16x+45y=215-16x + 45y = 215