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Consider the system of equations4x + 9y 165x - 3y 10Multiply every term in the second equation by some number so that the y-terms will have opposite coefficients,Write the new equation

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Step 1: Write the system of equations


\begin{gathered} 4x\text{ + 9y = 16} \\ 5x\text{ - 3y = 10} \end{gathered}

Step 2: Using Elimination method


\begin{gathered} 4x\text{ + 9y = 16 }\ldots\ldots\ldots\ldots\ldots..(1) \\ 5x\text{ -3y = 10 }\ldots\ldots\ldots\ldots\ldots\ldots(2) \\ m\mu\text{ltiply all equ (1) by coefficient of y in equ (2) and multiply all equ (2) by coefficient oy y in equ (1) } \\ *\text{ 3 (4x + 9y =16)} \\ *9\text{ (5x - 3y = 10)} \\ 12x\text{ + 27y = 48 }\ldots\ldots\ldots\ldots\ldots..(3) \\ 45x\text{ - 27y = 90} \end{gathered}

Hence the new equations are


\begin{gathered} 12x\text{ + 27y = 48 } \\ 45x\text{ - 27y = 90} \end{gathered}

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