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3x – 4y = 25 3x + 2y = 1 A. (1, –1) B. (3, –4) C. (–3, –9) D. (7, –1) Farmer Bob has pigs and chickens. He has 37 animals, and there are 124 legs among them altogether. How many chickens does Bob have? A. 25 B. 4 C. 12 D. –4 At a school supply store, binders cost $5 and pencil pouches cost $2. In one day, 42 of these items are sold for total sales of $144. Which system represents this (b represents binders and p represents pencil pouches), and how many binders were sold? A. b + p = 144 5b + 2p = 42 82 binders B. b + p = 42 2b + 5p = 144 22 binders C. b – p = 42 2b + 5p = 144 26 binders D. b + p = 42 5b + 2p = 144 20 binders Solve the system of equations. 3x – 7y = –13 –2x + 3y = 7 A. (–5, 1) B. (9, –2) C. (–2, 1) D. (1, –2) A system of two linear equations has an infinite number of solutions. How is this possible? A. It's not; the graphs of the two equations can intersect only once. B. The two equations are the same line. C. The equations are parallel lines. D. There was an error in solving the system. Which system has no solution? A. 4y = 2x – 6 B. 3x + 5y = 7 4x = 2y – 5 C. 2y = 4x + 2 D. 2x = 5y + 4 15y = 6x – 12 For which system of equations is (–2, 2) the solution? A. 3x – 5y = –16 –2x + 3y = 10 B. –4x + 2y = 6 2x – 3y = 10 C. 4x + 3y = 2 5x + 4y = –2 D. 6x + 5y = –2 –8x + 5y = –6 The perimeter of a rectangle is 48 cm. The length is 6 cm less than twice the width. Which system would model this situation, and what are the length and the width? A. 2l + 2w = 48 l + 2w = 6 Solution: (9, 6) B. 2l + 2w = 48 2l + w = –6 Solution: (–32, 56) C. l + w = 48 l – 2w = –6 Solution: (18, 6) D. 2l + 2w = 48 l – 2w = –6 Solution: (14, 10) For which system of equations is (–2, 3) the solution? A. 3x + 2y = 0 4x + 3y = –1 B. –3x + 4y = –6 2x + 5y = 11 C. –x + 7y = 16 5x – 3y = 16 D. –x + 7y = 23 5x + 3y = –1 What is the first step in solving this system of equations? 2x – 5y = 7 3x + 7y = –3 A. Multiply the first equation by 7 and the second by 2. B. Multiply the first equation by 3 and the second equation by –2. C. Add the equations together. D. Multiply the first equation by 2 and the second equation by 3.
For the first system of equations, use elimination. Multiply the second equation by 2 and add to the first equation. That'll give you x, then substitute the value of x in one of the original equations to get y.
for question 2 if it was c. 12 chicks times 2 legs = 24 legs... 124 legs - 24 legs = 100 legs... 100 legs / 4 legs is 25 pigs... 12 chickens + 25 pigs = 37 animals... BINGO! Question 2 the answer is C
For question 2, can also be answered by setting up a system of equations instead of guessing. P + C = 37 (P pigs + C chickens = 37 animals) 4P + 2C = 124 (4P pig legs + 2C chicken legs = 124 legs) Multiply the first equation by -4 and add to the second equation and solve for P.
the answer to #8 is d. because if you plug both of your values into x and y into both equations the answers will equal each other try it you can even use a calculator to make it easier