Question

[ 10x - 6y = 16

Elena is solving this system of equations: 50-3y = 8
She multiplies the second equation by 2, then subtracts the resulting equation from the first. To her surprise, she gets the
equation 0 = 0.
What is special about this system of equations? Why does she get this result and what does it mean about the solutions?
(If you are not sure, try graphing them.)
Type your response in the space below.

Answer 1

When the two equations are dependent, they have infinitely many solutions and represent the same line on a graph.

Step-by-step explanation:

When Elena multiplied the second equation by 2 and subtracted it from the first equation, she ended up with the equation 0 = 0. This means that the two equations are equivalent and represent the same line on a graph. In other words, the two equations are dependent, and they have infinitely many solutions.

The reason she gets this result is because the two equations have the same slope but different y-intercepts. When she subtracts the second equation from the first, the terms with y variables cancel out, leaving only 0 on both sides of the equation.

Graphically, this can be represented by two lines that intersect at every point on the line. This is because the two lines are parallel and have the same slope, indicating that they are the same line.

Learn more about Dependent systems of equations