Question

Graph the following system of equations.

3x + 6y = 12
3x + 2y = 8

What is the solution to the system?

A) There are infinitely many solutions.
B) There is one unique solution, (2, 1).
C) There is one unique solution, (6, 1).
D) There is no solution.

Answer 1

B: There is one unique solution, (2, 1)

Explanation:

Took the test.

Answer 2

B) There is one unique solution, (2, 1).

Attached is a graph of the system of equations.

Explanation:

Given system of equations:

`\begin{cases} 3x+6y=12 \\ 3x+2y=8\end{cases}`

Types of Solutions to a System of Equations

• Infinitely Many Solutions: when two lines overlap each other, causing their solutions to be infinite.
• One Solution: when two lines intersect only at one point.
• No Solution: when two lines do not intersect.

Using a graphing calculator, we can find the solution(s) to the given system of equations. To find the solution(s), we need to look at the point where the lines intersect; this is called the point of intersection.