Solve the system of equations: 3x+2y=240 3y-2x=35

Solve the system of equations:

Пошаговое решение:

1. Multiply the first equation by 2 and the second equation by 3 to eliminate x:

First equation * 2: \(2(3x + 2y) = 2(240) \Rightarrow 6x + 4y = 480\)

Second equation * 3: \(3(3y - 2x) = 3(35) \Rightarrow 9y - 6x = 105\)

2. Now, add the modified equations to eliminate x:

\((6x + 4y) + (9y - 6x) = 480 + 105 \Rightarrow 13y = 585\)

3. Solve for y:

\(13y = 585 \Rightarrow y = \frac{585}{13} = 45\)

4. Substitute the value of y into one of the original equations to solve for x. Let's use the first equation:

\(3x + 2(45) = 240 \Rightarrow 3x + 90 = 240\)

5. Solve for x:

\(3x = 240 - 90 \Rightarrow 3x = 150 \Rightarrow x = \frac{150}{3} = 50\)

Answer: x = 50, y = 45