Question

Can you explain how to find the solutions to the following system of equation problems?

Graph f(x) and g(x) to find the solution to the equation f(x) = g(x). Approximate the answer when necessary.

1. f(x) = -2/3x +4 and g(x)= x - 6
Ans:
Step1 graph lines. f(x) has y-int of 4 and slope of -2/3. g(x) has y-int of -6 and slope of 1.

Step2 look where lines intercept. point (6,0)

step3 check answer by substituting (6,0) into both f(x) and g(x)?
f(x): 0=-2/3(6) +4
0 = -4 +4
0 = 0 (solution)

g(x): 0 = 6 - 6
0 = 0

So, (6,0) is the solution to f(x) and g(x)

2. f(x) = -5/6x and g(x) = 2/5x + 4
Ans:
Step1 graph lines. f(x) has y-int of 0 and slope of -5/6. g(x) has y-int of 4 and slope of 2/5.

Step2 look where lines intercept. It's hard to tell. Estimated at (-3.1, 2.5).

step3 check answer by substituting (-3.1, 2.5) into both f(x) and g(x)?

f(x): 2.5 =-5/6(-3.1)
2.5 = -2.58 (not a solution?)

g(x): 2.5 = 2/5(-3.1)+ 4
2.5 = 1.24 + 4
2.5 = 5.24 (not a solution?)

So, (-3.1, 2.5) is not the solution to f(x) and g(x)?

Answer 1

#1, done well

#2, your sketch should look like this
http://www.wolframalpha.com/input/?i=plot+f(x)+%3D+-5%2F6x+,+g(x)+%3D+2%2F5x+%2B+4
look at the 2nd graph
looks like appr (-3.25, 2.5) to me, so your guess is close

your check:
f(x): 2.5 =-5/6(-3.1)
2.5 = -2.58 <----- should be +2.58, close enough

g(x): 2.5 = 2/5(-3.1)+ 4
2.5 = 1.24 + 4 <----- -1.24 + 4
2.5 = 2.76
had you used -3.25
2.5 = (2/5)(-3.25) + 4
2.5 = -1.3+4
2.5 = 2.7