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Solve the system of equations. {:[-2x+9y=11],[-5x+2y=-34],[x=◻],[y=◻]:}

Solve the system of equations.\newline−2x+9y=11−5x+2y=−34x=□y=□ \begin{array}{l} -2 x+9 y=11 \\ -5 x+2 y=-34 \\ x=\square \\ y=\square \end{array}

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Q. Solve the system of equations.\newline−2x+9y=11−5x+2y=−34x=□y=□ \begin{array}{l} -2 x+9 y=11 \\ -5 x+2 y=-34 \\ x=\square \\ y=\square \end{array}
  1. Multiply second equation: Multiply the second equation by a number that will allow us to eliminate one of the variables when added to the first equation. We can multiply the second equation by 22 to eliminate 'yy' when added to the first equation.\newline−2(−5x+2y)=−2(−34)-2(-5x + 2y) = -2(-34)\newline10x−4y=6810x - 4y = 68
  2. Add new equation to eliminate 'y': Add the new equation from Step 11 to the first equation to eliminate 'y'.\newline(−2x+9y)+(10x−4y)=11+68(-2x + 9y) + (10x - 4y) = 11 + 68\newline−2x+10x+9y−4y=79-2x + 10x + 9y - 4y = 79\newline8x+5y=798x + 5y = 79
  3. Solve for 'x': Solve the new equation from Step 22 for 'x'.\newline8x+5y=798x + 5y = 79\newlineSince we don't have a value for 'y' yet, we can't solve for 'x' directly. We need to find the value of 'y' first using the original equations.
  4. Multiply first equation: Multiply the first equation by a number that will allow us to eliminate 'xx' when added to the second equation. We can multiply the first equation by 55 to eliminate 'xx' when added to the second equation.\newline5(−2x+9y)=5(11)5(-2x + 9y) = 5(11)\newline−10x+45y=55-10x + 45y = 55
  5. Add new equation to eliminate 'x': Add the new equation from Step 44 to the second equation to eliminate 'x'.\newline(−10x+45y)+(−5x+2y)=55−34(-10x + 45y) + (-5x + 2y) = 55 - 34\newline−10x−5x+45y+2y=21-10x - 5x + 45y + 2y = 21\newline−15x+47y=21-15x + 47y = 21
  6. Solve for 'y': Solve the new equation from Step 55 for 'y'.\newline−15x+47y=21-15x + 47y = 21\newlineWe made a mistake in the previous step; we should have added the equations to eliminate 'x', not subtracted them. Let's correct this.\newline(−10x+45y)+(−5x+2y)=55+(−34)(-10x + 45y) + (-5x + 2y) = 55 + (-34)\newline−10x−5x+45y+2y=55−34-10x - 5x + 45y + 2y = 55 - 34\newline−15x+47y=21-15x + 47y = 21\newlineThis is still incorrect; the correct equation should be:\newline−15x+47y=21-15x + 47y = 21

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