Question

determine whether the system has no solution, one solution, or infinitely many solutions. if the system has one solution, name it
x + y = 5
3x + 5y = 15
100 characters remaining

Explanation:

Step1: Solve the first equation for x

From \( x + y = 5 \), we can express \( x \) as \( x = 5 - y \).

Step2: Substitute x into the second equation

Substitute \( x = 5 - y \) into \( 3x + 5y = 15 \):

$$
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$$

Step3: Solve for y

Subtract 15 from both sides:

$$ 2y = 15 - 15\\ 2y = 0\\ y = 0 $$

Step4: Solve for x

Substitute \( y = 0 \) into \( x = 5 - y \):
\( x = 5 - 0 = 5 \)

Since we found a unique solution \( (x, y) = (5, 0) \), the system has one solution.

Answer:

The system has one solution, which is \( x = 5 \), \( y = 0 \) (or the ordered pair \( (5, 0) \)).