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Solve the system of equations. {:[-9y+4x-20=0],[-7y+16 x-80=0],[x=◻],[y=◻]:}

Solve the system of equations.\newline−9y+4x−20=0−7y+16x−80=0x=□y=□ \begin{array}{l} -9 y+4 x-20=0 \\ -7 y+16 x-80=0 \\ x=\square \\ y=\square \end{array}

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Q. Solve the system of equations.\newline−9y+4x−20=0−7y+16x−80=0x=□y=□ \begin{array}{l} -9 y+4 x-20=0 \\ -7 y+16 x-80=0 \\ x=\square \\ y=\square \end{array}
  1. Write Equations: Write down the system of equations.\newlineWe have the following system of equations:\newline−9y+4x−20=0-9y + 4x - 20 = 0\newline−7y+16x−80=0-7y + 16x - 80 = 0
  2. Rearrange Equations: Rearrange the equations to align the variables.\newlineLet's rearrange the equations to make it easier to apply the elimination method:\newline4x−9y=204x - 9y = 20\newline16x−7y=8016x - 7y = 80
  3. Eliminate Variable: Identify the variable to eliminate.\newlineWe will eliminate 'xx' by finding a multiplier for the first equation that will make the coefficient of 'xx' in the first equation the same as the second equation when multiplied.
  4. Find LCM of Coefficients: Find the least common multiple (LCM) of the coefficients of 'xx'.\newlineThe coefficients of 'xx' are 44 and 1616. The LCM of 44 and 1616 is 1616. We need to multiply the first equation by 44 to get the coefficient of 'xx' to be 1616.
  5. Multiply and Rewrite: Multiply the first equation by 44 and rewrite the system.\newlineMultiplying the first equation by 44 gives us:\newline(4x−9y)×4=20×4(4x - 9y) \times 4 = 20 \times 4\newline16x−36y=8016x - 36y = 80\newlineNow our system looks like this:\newline16x−36y=8016x - 36y = 80\newline16x−7y=8016x - 7y = 80
  6. Subtract Equations: Subtract the second equation from the first to eliminate 'x'.\newline(16x−36y)−(16x−7y)=80−80(16x - 36y) - (16x - 7y) = 80 - 80\newlineThis simplifies to:\newline−36y+7y=0-36y + 7y = 0\newline−29y=0-29y = 0
  7. Solve for y: Solve for yy.\newlineDivide both sides by −29-29 to find the value of yy:\newliney=0−29y = \frac{0}{-29}\newliney=0y = 0
  8. Substitute and Solve for x: Substitute y=0y = 0 into one of the original equations to solve for 'xx'.\newlineLet's use the first original equation:\newline4x−9(0)=204x - 9(0) = 20\newline4x=204x = 20
  9. Solve for x: Solve for xx.\newlineDivide both sides by 44 to find the value of xx:\newlinex=204x = \frac{20}{4}\newlinex=5x = 5
  10. Write Solution: Write the solution as a coordinate point.\newlineThe solution to the system of equations is (x,y)=(5,0)(x, y) = (5, 0).

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