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Solve the system. 3y=6+x, 3x-9y=9

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Answer:

The system of linear equations has no solution.

Explanation:

We can solve the system of linear equations using substitution or elimination method.

Here's how you can solve it using substitution:

Solve one equation for either x or y.

Substitute the expression you found in step 1 into the other equation.

Solve for the remaining variable.

Use the values you found in steps 3 to find the other variable.

Starting with the first equation:

3y = 6 + x

Solving for x:

x = 3y - 6

Next, we substitute this expression into the second equation:

3x - 9y = 9

Plugging in x = 3y - 6:

3(3y - 6) - 9y = 9

Expanding the left-hand side:

9y - 18 - 9y = 9

Combining like terms:

0y - 18 = 9

Adding 18 to both sides:

0y = 27

Since y cannot equal 0, we have a contradiction and the system has no solution.

So, the system of linear equations has no solution.

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