Question: 9) \begin{cases} 4x - 5y = 9 \\ 5x - 6y = 9 \end{cases}
Solution
To solve the system of equations, we have: {4x−5y=95x−6y=9 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 x. {5(4x−5y)=5(9)4(5x−6y)=4(9) This gives: {20x−25y=4520x−24y=36 Subtract the second equation from the first: (20x−25y)−(20x−24y)=45−36 Simplify: −25y+24y=9 −y=9 Divide by −1: y=−9 Now substitute y=−9 back into the first equation: 4x−5(−9)=9 Simplify: 4x+45=9 Subtract 45 from both sides: 4x=9−45 4x=−36 Divide by 4: x=−9 The solution to the system of equations is x=−9 and y=−9.