Question

heather writes the equations below to represent two lines drawn on the coordinate plane. –6x 18y = 0 4x – 12y = 20 after applying the linear combination method, heather arrived at the equation 0 = 60. what conclusion can be drawn about the system of equations? the equation has no solution; therefore, the system of equations has no solution. the equation has a solution at (0, 60); therefore, the system of equations has a solution at (0, 60). the equation has infinite solutions; therefore, the system of equation as infinite solutions. the equation has a solution at (0, 0); therefore, the system of equations has a solution at (0, 0).

Answer 1

The correct answer is:

The equation has no solution; therefore, the system of equations has no solution.

Explanation:

When solving a system of equations, after we combine the equations, if we find that there is no solution, that means that there is no solution to the entire system of equations.

Answer 2

In this example the equation has no solution. This is because, in algebra, the variables are what is solved for. Here, through the combination method, Heather has determined that 0 = 60, which is not true. Zero cannot equal a number other than itself; additionally there are no variables that were solved for in this equation. By this it is meant that "x" is not given a value and "y" is not given a value. These two values would be used for coordinates to plot the line on a graph