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Classify the system of equations 1/3x+y+5=0 1/2x+y-3=0

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Final answer:

The system of equations can be classified as consistent and independent, meaning they have a unique solution. By using the method of elimination, we can find that x = 9/2 and y = -3/2 are the solutions to the system of equations.

Step-by-step explanation:

The system of equations can be classified as consistent and independent. This means that the equations have a unique solution, which can be found by solving them simultaneously. To do this, we can use the method of elimination or substitution. Let's use the method of elimination:

Multiply the first equation by 2 to eliminate the fraction: 2(1/3x+y+5) = 2(0) becomes 2/3x+2y+10 = 0

Multiply the second equation by 3 to eliminate the fraction: 3(1/2x+y-3) = 3(0) becomes 3/2x+3y-9 = 0

Now we can subtract the two equations to eliminate the y term: (2/3x+2y+10) - (3/2x+3y-9) = 0

Simplify the equation: 2x-9 = 0

Solve for x: x = 9/2

Substitute the value of x into either of the original equations to solve for y. Let's use the first equation: 1/3(9/2) + y + 5 = 0

Simplify the equation: 3/2 + y + 5 = 0

Solve for y: y = -3/2

Therefore, the solution to the system of equations is x = 9/2 and y = -3/2.

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