Question

Consider the following system:

x=2y+5
4x-8y=20

When solving this system by the substitution method, 20=20 is obtained. What is the solution set?

A.
The solution set is ​{}. ​(Type an ordered​ pair.)
B.
There are infinitely many solutions. The solution set is (x,y) or ​(x,y)
C.
The solution is empty set.

If the system is solved by​ graphing, two lines that
A. are identical (or coincide)
B. are perpendicular
C. are parallel
will be obtained.

Answer 1

The systems of equation are identical and such there are infinitely many solutions. For the first part the correct answer is B. For the second part, the correct answer is A

Explanation:

If we multiply the first equation by 4 the result is the second equation and thus the systems of equations are scalar multiples of each other. The solution to such a system is found by expressing one variable in terms of the other hence choice B.

Since the systems are scalar multiples of each other, if we graph them they would simply coincide since they are identical, that is they have same slope and y-intercept.