Question

Without solving, determine the number of solutions for this system. What does the graph of the system look like?

Answer 1

Rewriting each equation in slope-intercept form, you have

... y = (3/2)x -5/4

... y = (3/2)x - 5/6

These lines have the same slope, but different intercepts. The appropriate description is ...

... A) no solution; parallel lines

Answer 2

Answer:Correct

no solution; parallel lines

You can determine the number of solutions for the system without solving by rewriting the equations in standard form and simplifying.

Rewrite the equations in standard form:

6x - 4y = 5

9x - 6y = 5

Factor out the GCF for each equation:

2(3x - 2y) = 5

3(3x - 2y) = 5

Simplify:

3x - 2y =  

5

2

3x - 2y =  

5

3

3x -2y cannot equal both  

5

2

and  

5

3

. Therefore the system doesn't have any solutions.