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 Subject: Algebra questions Category: Miscellaneous Asked by: cleanncrazi-ga List Price: \$40.00 Posted: 15 Jun 2004 22:21 PDT Expires: 15 Jul 2004 22:21 PDT Question ID: 361720
 ```1. Give the solution to y in the system: y = 9 ? 2x and 2x ? 5y = 15. A) y=1 B) y=5 C) D) y=?1 2. Give the solution to x in the system: 3x + 2y = 3 and 63x ? 36y = 11. A) x=2 B) C) D) 3. Sesame Street on Stage has different ticket prices for adults and for children under 6. Beth and her two children, ages 3 and 4, paid \$15 to gain entrance, while Jamie and John Jacobs and their 2-year-old daughter got in for \$19.50. What is the ticket price for adults? A) \$3.50 B) \$5.75 C) \$8.00 D) \$9.00 4. Solve the system for y. 2x + y = 3 2x + y = ?1 A) Inconsistent B) y= 2 C) y= ?3 D) y=4 5. Solve the system for x. 2x + 3y = 1 5x + 3y = 16 A) x=2 B) x=0 C) x=5 D) x=?3 6. Solve the system for y. ?7x + y = 12 5x ? 9y = 8 A) y= 2 B) y=?2 C) y=4 D) Dependent 7. Solve the system for x x + y = 2 x = 4y + 5 A) x=13/5 B) x=?3/5 C) x=?13/5 D) x=3/5 8. Solve the system for y. x + y = ?3 x ? 2y = ?5 A) y= 2/3 B) y=?11/4 C) y= ?3 D) y=1/5 9. Solve the system for y. ?3x ? y = ?4 ?3x ? 7y = ?3 A) y=?25/18 B) y= ?4/6 C) y=?1/12 D) y=?1/6 10. Solve the system for x. ?4x + 2y = ?5 2x ? 4y = 3 A) x=7/6 B) x=?1/2 C) x=4/6 D) x=7 11. The definition of an inconsistent system could be A) A system where two equations are the same line B) A system of independent equations C) A system of parallel lines D) A system of two inequalities 12. The system 4x ? 24y = 32 and x ? 6y = 8 has no solution. A) True B) False 13. Find the point of intersection of the horizontal line through the point (3, ?2) and the line whose equation is 2x ? 3y = 6. A) (3, 0) B) (3, ?4) C) (3, ?2) D) (0, ?2) 14. If two lines intersect in a single point, a system consisting of these two linear equations is: A) dependent B) inconsistent C) independent D) systematic```
 Subject: Re: Algebra questions Answered By: tox-ga on 15 Jun 2004 23:17 PDT Rated:
 ```Hi cleanncrazi! I will post the answers right now, to get them to you as fast as possible, and I will immediately follow that up with a clarification with the step by step method of finding those answers. 1. D) y = -1 2. x = 5/9 3. C) \$800 4. A) Inconsistent 5. C) x = 5 6. B) y = -2 7. A) x= 13/5 8. A) y= 2/3 9. D) y= ?1/6 10. A) x=7/6 11. C) A system of parallel lines 12. B) False 13. D) (0, ?2) 14. C) Independent Cheers, tox-ga``` Clarification of Answer by tox-ga on 16 Jun 2004 00:01 PDT ```Hi! Sorry, there is a slight typo in my answer to question 3. I forgot the decimal point; the answer is C) \$8.00, not eight hundred dollars. Here are some step-by-step solutions. 1. First, isolate x in each equation: y = 9 ? 2x => 2x = 9 - y 2x ? 5y = 15 => 2x = 15 + 5y Now 2x = 2x, so we can eliminate that variable: 9 - y = 15 + 5y and now solve for y 6y = -6 -> y = -1 2. We use essentially the same method: isolate a variable and eliminate it 3x + 2y = 3 => y = -1.5x + 1.5 63x ? 36y = 11 => y = 63/36x - 11/36 (after dividing by -36 and moving the x) 63/36x - 11/36 = -1.5x + 1.5 117/36x = 65/36 x = 65/117 = 5/9 3. let a = the price an adult pays let c = the price a child pays Beth and her two children, ages 3 and 4, paid \$15... this means that an adult ticket and 2 child tickets cost 15 so: a + 2c = 15 Jamie and John Jacobs and their 2-year-old daughter got in for \$19.50 so: 2a + c = 19.5 Solving these two equations using the same method as above (isolate and eliminate c) we get a = 8 So the adult pays \$8. 4. Solving for y means we should isolate and eliminate x 2x + y = 3 => 2x = -y + 3 2x + y = ?1 => 2x = -y - 1 -y + 3 = -y - 1 add y to both sides and we get 3 = -1 this is clearly impossible, so that means no pair of numbers x and y could satisfy the system of equations. This means it is inconsistent. 5. 2x + 3y = 1 => 3y = -2x + 1 5x + 3y = 16 => 3y = -5x + 16 2x - 1 = 5x - 16 3x = 15 -> x = 5 6 to 10 is essentially more of the same, isolating and eliminating variables. If you would like some help with the steps to these, just ask and I'll be glad to provide it. 11. An inconsistent system is one with no solutions. In terms of two lines, it would be two lines which do not cross ever. This means the lines are parallel. 12. Notice that 4x ? 24y = 32 is just four times x ? 6y = 8 so really, these describe the same line. That means this system has infinitely many solutions, not no solutions. False. 13. The horizontal line running through (3, -2) is y = -2. Solving y = -2 and 2x ? 3y = 6 we get 2x ? 3(-2) = 6 => 3x + 6 = 6 => x = 0 so the point is (0,-2) 14. If two lines intersect at a single point, - they are not dependent, since dependent lines intersect at infinitely many points - they are not inconsistent, since inconsistent lines do not intersect - to be honest, I have no idea what 'systematic' could mean but they definitely are independent, as independent lines intersect at one point. Cheers, tox-ga```
 cleanncrazi-ga rated this answer: `This was wonderful!!!!!!!!`

 Subject: Re: Algebra questions From: jazar-ga on 16 Jun 2004 02:07 PDT
 ```Ahah, the Joy of Internet.... If you don't have a big brother or a big sister to do the homework for you, you have google now.```
 Subject: Re: Algebra questions From: hadj-ga on 16 Jun 2004 03:07 PDT
 `I agree with you, Jazar :)`
 Subject: Re: Algebra questions From: scubajim-ga on 16 Jun 2004 09:36 PDT
 ```If I was a teacher I would be looking at these boards and usenet for this type of thing. Then in class I would point out that I had found someone doing this. It doesn't promote learning.```
 Subject: Re: Algebra questions From: saem_aero-ga on 16 Jun 2004 09:54 PDT
 `I guess for 40 doller's the google researcher looked past the TOS.`
 Subject: Re: Algebra questions From: mralex-ga on 16 Jun 2004 11:15 PDT
 ```Scubajim: And if were an English teacher, I'd point out that your sentence should read, "If I were a teacher..."```