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img of 9) \begin{cases} 4x - 5y = 9 \\ 5x - 6y = 9 \end{cases}

Question: 9) \begin{cases} 4x - 5y = 9 \\ 5x - 6y = 9 \end{cases}

Solution

To solve the system of equations, we have: {4x5y=95x6y=9 \begin{cases} 4x - 5y = 9 & \\ 5x - 6y = 9 & \end{cases} First, let’s use the method of elimination. Multiply the first equation by 5 and the second equation by 4 to align the coefficients of xx. {5(4x5y)=5(9)4(5x6y)=4(9) \begin{cases} 5(4x - 5y) = 5(9) & \\ 4(5x - 6y) = 4(9) & \end{cases} This gives: {20x25y=4520x24y=36 \begin{cases} 20x - 25y = 45 & \\ 20x - 24y = 36 & \end{cases} Subtract the second equation from the first: (20x25y)(20x24y)=4536 (20x - 25y) - (20x - 24y) = 45 - 36 Simplify: 25y+24y=9 -25y + 24y = 9 y=9 -y = 9 Divide by 1-1: y=9 y = -9 Now substitute y=9y = -9 back into the first equation: 4x5(9)=9 4x - 5(-9) = 9 Simplify: 4x+45=9 4x + 45 = 9 Subtract 45 from both sides: 4x=945 4x = 9 - 45 4x=36 4x = -36 Divide by 4: x=9 x = -9 The solution to the system of equations is x=9x = -9 and y=9y = -9.

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