Question

problem 7
this graph shows the lines for these equations:
3y=3x + 6
y = x + 2
how many solutions are there for this system of equations?
○ no solutions
○ one solution
○ infinite solutions

Explanation:

Step1: Simplify the first equation

Given the equation \( 3y = 3x + 6 \), divide both sides by 3.
\( \frac{3y}{3}=\frac{3x + 6}{3} \) simplifies to \( y = x + 2 \).

Step2: Compare the two equations

The second equation is also \( y = x + 2 \). This means both equations represent the same line.

Step3: Determine the number of solutions

When two linear equations represent the same line, every point on the line is a solution to both equations. So, there are infinite solutions.

Answer:

Infinite solutions (the option: Infinite solutions)