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Find the solution of the system of equations. {:[-3x+4y=-7],[3x+6y=27]:} (_________,________)"

Find the solution of the system of equations.\newline−3x+4yamp;=−73x+6yamp;=27 \begin{aligned} -3 x+4 y & =-7 \\ 3 x+6 y & =27 \end{aligned} \newline(_________,________)

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Full solution

Q. Find the solution of the system of equations.\newline−3x+4y=−73x+6y=27 \begin{aligned} -3 x+4 y & =-7 \\ 3 x+6 y & =27 \end{aligned} \newline(_________,________)
  1. Add Equations Together: Add the two equations together to eliminate xx. (−3x+4y)+(3x+6y)=−7+27\ (-3x + 4y) + (3x + 6y) = -7 + 27
  2. Simplify Equation: Simplify the equation. 4y+6y=204y + 6y = 20
  3. Combine Like Terms: Combine like terms. 10y=2010y = 20
  4. Divide to Solve for y: Divide both sides by 1010 to solve for y.\newliney=2010y = \frac{20}{10}
  5. Calculate y Value: Calculate the value of y.\newliney = 22
  6. Substitute yy into Equation: Substitute y=2y = 2 into one of the original equations to solve for xx. Let's use the first equation: −3x+4y=−7-3x + 4y = -7.\newline−3x+4(2)=−7-3x + 4(2) = -7
  7. Multiply and Subtract: Multiply 44 by 22.
    −3x+8=−7-3x + 8 = -7
  8. Combine Numbers: Subtract 88 from both sides.\newline−3x=−7−8-3x = -7 - 8
  9. Divide to Solve for x: Combine the numbers on the right.\newline−3x=−15-3x = -15
  10. Calculate x Value: Divide both sides by −3-3 to solve for xx.\newlinex=−15−3x = \frac{-15}{-3}
  11. Calculate xx Value: Divide both sides by −3-3 to solve for xx.x=−15−3x = \frac{-15}{-3}Calculate the value of xx.x=5x = 5

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