Based on the graph of the following system of equations, determine the number of solutions.

2x + 3y = 9
6y = 5 − 4x

A. No solutions
B. Exactly one solution
C. Exactly two solutions
D. Infinitely many solutions

Write these as
y=-(2/3)x+3
y=-(4/6)x+5=-(2/3)x+5.

These are straight lines with the same slope
of -2/3 and hence are parallel. SInce the
y-interecepts differ, they are different lines
and hence do not intersect.
No solutions -A.

I am assuming you have some working knowledge of lines...

You should solve them both for y and express the lines as y=Mx+b . M is the slope of the line and b the Y intercept.

If the M's and b's are the same for both, they are the same line and therefore cross everywhere...infintely many solutions

If the M's are the same but the b's are different, they are parallel lines and do not cross at all and therefore.... no solution

If the M's are different the slopes are different and the lines must cross somewhere.... one solution

Hope this helps!

since both variables x and y are first power, the graph must be straight line and straight line graph only has one solution.

If it is second power, the answer may vary and you have to draw a graph.

A. No solution as the two lines are parallel.