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Find the solution of the system of equations. {:[-8x+9y=39],[8x-10 y=-46]:}(_________,________)"

Find the solution of the system of equations.\newline−8x+9yamp;=398x−10yamp;=−46 \begin{aligned} -8 x+9 y & =39 \\ 8 x-10 y & =-46 \end{aligned} \newline(_________,________)

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Full solution

Q. Find the solution of the system of equations.\newline−8x+9y=398x−10y=−46 \begin{aligned} -8 x+9 y & =39 \\ 8 x-10 y & =-46 \end{aligned} \newline(_________,________)
  1. Combine Equations: Add the two equations together to eliminate xx.(−8x+9y)+(8x−10y)=39+(−46)(-8x + 9y) + (8x - 10y) = 39 + (-46)
  2. Simplify Equation: Simplify the equation. −8x+8x+9y−10y=39−46-8x + 8x + 9y - 10y = 39 - 46
  3. Combine Like Terms: Combine like terms.\newline0x−y=−70x - y = -7
  4. Solve for y: Solve for y.\newliney=7y = 7
  5. Substitute yy into Equation: Substitute y=7y = 7 into one of the original equations to solve for xx. Let's use the first equation: −8x+9(7)=39-8x + 9(7) = 39
  6. Multiply and Simplify: Multiply 99 by 77.
    −8x+63=39-8x + 63 = 39
  7. Subtract to Solve: Subtract 6363 from both sides.\newline−8x=39−63-8x = 39 - 63
  8. Simplify Right Side: Simplify the right side.\newline−8x=−24-8x = -24
  9. Divide to Solve: Divide both sides by −8-8.\newlinex=−24−8x = \frac{-24}{-8}
  10. Calculate xx: Calculate the value of xx.x=3x = 3

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