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Solve the following linear system of equations: \( 5 x+y=53 \) \( 3 x-9 y=3 \) \( x=\square \) \( y=\square \)

Ask by Tran Elliott. in Canada
Mar 14,2025

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\( x = 10 \) and \( y = 3 \).

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To solve the system of equations, let's first rewrite them: 1. \( 5x + y = 53 \) 2. \( 3x - 9y = 3 \) From the first equation, we can express \( y \) in terms of \( x \): \( y = 53 - 5x \) Now, substitute this expression for \( y \) into the second equation: \( 3x - 9(53 - 5x) = 3 \) Distributing the -9: \( 3x - 477 + 45x = 3 \) Combine like terms: \( 48x - 477 = 3 \) Add 477 to both sides: \( 48x = 480 \) Now divide by 48: \( x = 10 \) Now, plug \( x = 10 \) back into the equation for \( y \): \( y = 53 - 5(10) \) \( y = 53 - 50 = 3 \) Therefore, the solution to the system is: \( x = 10 \) \( y = 3 \)

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