Question

solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. if the system has one solution, find the solution.
\

$$\begin{cases} 2x + 2y = 18 \\\\ x + y = 9 \\end{cases}$$

answer
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\bigcirc one solution \quad \quad (\boxed{\quad}, \boxed{\quad})
\bigcirc no solution
\bigcirc infinite number of solutions

Explanation:

Step1: Simplify the first equation

Divide the first equation \(2x + 2y = 18\) by 2, we get \(x + y = 9\), which is the same as the second equation.

Step2: Analyze the system

Since the two equations are actually the same line (they represent the same linear relationship), every point on the line \(x + y = 9\) is a solution. So the system has an infinite number of solutions.

Answer:

Infinite Number of Solutions