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Which statement is true about the system x + 3y = 11 and y = x - 7?

User Dejv
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1 Answer

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The given system of equations is:

1) x + 3y = 11

2) y = x - 7

To determine which statement is true about this system, we can solve the equations by substitution or elimination:

Using the substitution method:

1) Substitute the value of y from equation 2 into equation 1:

x + 3(x - 7) = 11

Simplify:

x + 3x - 21 = 11

Combine like terms:

4x - 21 = 11

Add 21 to both sides:

4x = 32

Divide by 4:

x = 8

Substitute x = 8 into equation 2 to find y:

y = 8 - 7

y = 1

Therefore, the solution to the system of equations is x = 8 and y = 1.

Now, let's analyze the statements:

Statement 1: The system has no solution.

This statement is false because we have found a unique solution for the system, which is x = 8 and y = 1.

Statement 2: The system has infinitely many solutions.

This statement is false because we have found a single solution for the system, not infinitely many.

Statement 3: The system has exactly one solution.

This statement is true because we have found one unique solution for the system, which satisfies both equations.

In summary, statement 3 is true: The system x + 3y = 11 and y = x - 7 has exactly one solution, which is x = 8 and y = 1

User Hraban
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