Are the equations y=2x+5 and y=5x+2 consistent, inconsistentt,ordependent? [A] c

Question

Are the equations y=2x+5 and y=5x+2 consistent, inconsistentt,ordependent? [A] consistent [B] inconsistent [C] dependant [D] Both A and C
There were 16 more nickels than dimes in the purse. If therewere100 coins total, how many nickels werethere? [A] 42 [B] 2.90 [C] 16 [D] 84 (This one is wrong.) [E] None of these Are the equations y=2x+5 and y=5x+2 consistent, inconsistentt,ordependent? [A] consistent [B] inconsistent [C] dependant [D] Both A and C
There were 16 more nickels than dimes in the purse. If therewere100 coins total, how many nickels werethere? [A] 42 [B] 2.90 [C] 16 [D] 84 (This one is wrong.) [E] None of these Are the equations y=2x+5 and y=5x+2 consistent, inconsistentt,ordependent? [A] consistent [B] inconsistent [C] dependant [D] Both A and C
There were 16 more nickels than dimes in the purse. If therewere100 coins total, how many nickels werethere? [A] 42 [B] 2.90 [C] 16 [D] 84 (This one is wrong.) [E] None of these

Explanation / Answer

Definition 6.2 A system is underdetermined when there are an infinite number of solutions

Definition 6.3 A system is inconsistent if it has no solutions.

Definition 6.4 A system is uniquely determined if there is exactly one solution to the system.

Remark 17 Many pre-calculus texts refer to underdetermined systems as dependent systems and to uniquely determined systems as independent systems.

If you graph the two equations, you will see they intersect at one point.

This makes them consistent, which is A.

Since there is only one solution, it cannot be dependent which eliminates C a

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