AbeNeedsAnswers wrote:y = ax - 5
y = x + 6
y = 3x + b
In the xy-plane, the straight-line graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?
(1) a = 2
(2) r = 17
D
We can begin by substituting p and r for x and y, respectively, in the three given equations.
1) r = ap - 5
2) r = p + 6
3) r = 3p + b
Statement One Alone:
a = 2
We can substitute 2 for a in the equation r = ap - 5. Thus, we have:
r = 2p - 5
Next we can set equations 1 and 2 equal to each other.
2p - 5 = p + 6
p = 11
Since p = 11, we see that r = 11 + 6 = 17
Finally, we can substitute 11 for p and 17 for r in equation 3. This gives us:
17 = 3(11) + b
17 = 33 + b
-16 = b
Statement one alone is sufficient to answer the question.
Statement Two Alone:
r = 17
We can substitute r into all three equations and we have:
1) 17 = ap - 5
2) 17 = p + 6
3) 17 = 3p + b
We see that p = 11. Now we can substitute 11 for p in equation 3 to determine a value for b.
17 = 3(11) + b
-16 = b
Statement two alone is also sufficient to answer the question.
Answer:
D
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