Question

lesson 17
solutions does this system of equations have?
you know.
\

$$\begin{cases} y + \\frac{2}{3}x = 4\\\\ 2x = 12 - 3y \\end{cases}$$

Explanation:

Step1: Rewrite the first equation

Rewrite \( y + \frac{2}{3}x = 4 \) in standard form. Multiply through by 3 to eliminate the fraction: \( 3y + 2x = 12 \), which can be rearranged as \( 2x = 12 - 3y \).

Step2: Compare with the second equation

The second equation is \( 2x = 12 - 3y \). Notice that both equations are identical (they represent the same line).

Step3: Determine the number of solutions

When two equations in a system represent the same line, there are infinitely many solutions because every point on the line satisfies both equations.

Answer:

The system of equations has infinitely many solutions.