Question

Compare the slopes and y-intercepts for the equations in this system of equations. How many solutions does this system of equations have? 2 Y +6 2 Y 2 +6 A One solution B No solution Infinitely many solutions

Answer 1

Solution of a system of equations

We want to know if there is any form for both equations to have the same x and y.

$\begin{gathered} y=\frac{2}{3}x+6 \\ \text{and} \\ y=\frac{2}{3}x+6 \end{gathered}$

There are three possibilities:

1. There is only one x and y value that satisfy both equations.

2. There is none x and y value that satisfy both equations.

3. Every x and y values that satisfy one equation, satisfy the other equation too.

How many solutions has the system?

If it is the case 1, the system have only one solution.

If it is the case 2, the system have no solution.

If it is case 3, the system have infinite solutions.

In this case both lines are the same. This means that they have the same points, they share infinite points. This is, for all x and y they will be the same.

each coordinate of the line

y = 2/3x + 6

is a solution for both equations

Answer: they have infinite solutions