Question

1. what is the solution to this system of equations? \\(\

$$\begin{cases} 2(x + 4) + 3y = 23 \\\\ 5 + 3y = 20 - 2x \\end{cases}$$

\\) a (5, 7.5) b 7.5 c no solutions d infinitely many solutions

Explanation:

Step1: Simplify the first equation

Expand \(2(x + 4)+3y = 23\): \(2x+8 + 3y=23\), then \(2x + 3y=23 - 8=15\), so \(2x+3y = 15\).

Step2: Simplify the second equation

Rearrange \(5 + 3y=20 - 2x\): \(2x+3y=20 - 5 = 15\), so \(2x + 3y=15\).

Step3: Analyze the two equations

Both equations simplify to \(2x + 3y=15\), which means they are the same line. So there are infinitely many solutions.

Answer:

D Infinitely Many Solutions