Question

PLEASE HELP ME .......

Which of the following statements describe the system
{y=3x+2y=y−2x−1? Select two answers.
A.consistent
B.inconsistent
C.infinite solutions
D.one solution

Answer 1

A.consistent

D.one solution

Explanation:

Assuming the system has equations

`y=3x+2\\y=2x-1`

Then we can examine the gradients to make our choice without necessarily solving the equations.

Interestingly, both equations are in slope-intercept form. (y=mx+c) where m=3 is the slope of the first equation and m=2 is the slope of the second equation.

Since the slopes are not the same the lines are not parallel.

Non-parallel lines in the same plane will meet at only one point, there is only one solution.

The system is consistent because there exist a solution.