Question

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

6x = 4y + 5
6y = 9x - 5
A) no solution; parallel lines
B) infinite solutions; one line
C) one solution; intersecting lines
D) two solutions; intersecting lines

Answer 1

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.

Answer 2

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