Question

Three students are working to find the solution set of this system of equations:

y = x - 6
4y = 4x - 20
Use the drop-down menus to complete the statements about each of their methods.
a) Student 1 will use the elimination method.
b) Student 2 will use the substitution method.
c) Student 3 will use graphing.
d) None of the above

Answer 1

The question discusses three methods to solve a system of linear equations: elimination by Student 1, substitution by Student 2, and graphing by Student 3. Each method involves different steps, but all aim to find where the two equations intersect, which is the solution set.

Step-by-step explanation:

The question inquires about methods used to solve a system of linear equations. These equations, y = x - 6 and 4y = 4x - 20, can be solved by various techniques. Each student chooses a different method.

1. Student 1 uses the elimination method.
2. Student 2 opts for the substitution method.
3. Student 3 employs graphing to find the solution set.

Through the elimination method, one could multiply the first equation by 4 to match the coefficients of y and then subtract the equations to cancel out y.

For substitution, since y is already isolated in the first equation, it can be put into the second equation in place of y.

The graphing method involves plotting both equations on a graph and observing where they intersect to determine the solution set.