8x+12y=108

~- ~ OAU l » iiiwmiim *' » . . wi . fcifcfc.mupt i IkM’eAO Wc m £-^ . k 1 Which ot the following number lines shows the solution to the inequality given below? \ X£ - \0 - 4x + 7 < 33 OR 4* + 4 > -16 H X 7 - 3 C> y > -O o -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 o -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 o -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 o O B. » C -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 0 2 4 0 2 4 0 2 4 2. Solve for x in the two equations below using substitution. 4* - ( 2x O .A. X OB. 1 O C. x OD “ “ + + 2 j=6 2y =7 a% ~ - I 1 2 X • 1'. 2 - .1 ^ 3 < 13* ~ 2 1 ~ , | 13 6 3. The freshman class is planning a field trip. The class can either visit the aviation museum or the local arboretum . At the aviation museum , tickets cost $ 18 each, plus a flat rate of $54 for parking all the buses. At the arboretum, tickets cost $12 each, plus a flat rate of $61 for parking all the buses. Let x represent the number of people going on the field trip, and let y represent the total cost of the field trip. Which system' of equations could be used to find how many people can go on either field trip so that both field trips have the » same cost? • y O A. y = 18* + = 12 x + $54 $61 - ) 2 * +- 5 M ) 3 i + (D \i I \j - i t d ( y t y o B. y - 54* + $18 y O C. y = 18 + $12 — 54 x + $61 y OD y = 12x + $54 = eix + $12 ® - = i8r + $61 N a t s * 5 S 4. Solve for x . O A.1 = -6 o .x “ Oc.1 = -10 O D. x —2 V s B * < , t ' 8 x -f 6 = 5^ S X +- (o 4 xvC 10 ? 3 - 6 x + 24 * + 3M - - 3 *-( x~ 3 5. Use elimination to find the solution to the system of equations. » Mr K -v 3 My c? 3 (S x + i y O A. 1" — 23 2’ y = -76 ) - $ ( 3 x + 7 y = -34 ) = -/ - g^ \ 4 O D. 1 " -30, y = |; 8 6. Use elimination to find the solution to the system of equations. 3 (9® + 2 y = -50 ~ 4 (2* + 9y = 6 } o s A. ^ 8 9 ^ ~ 4 \i ^ - \oo < - XKj - - 5 4 K^ . Q V = 0, y = -19 x -9, y = -1 O c. = 1 O B. ^ . 33g o B. x = 3> y y = -77 39 o c. x - 2 * v - 5 oo.1 = -6,T= T “ L s V 5 3x _ ' . 3 (-2i < 7 Solve for v in the two equations below using substitution . ; i s i * 3 ( - '0 3C ) “ G>\/ V = 12 O B. = 18 24 a? - Mi = 72 48a? -f 4 t/ = 360 13 * - - G> - (c \ ~ Q, j l O A.1 o c.1 = O D. r = (c \j 2 8. Solve for x in the two equations below using substitution . 1 ' ' - \ X- Oc o D. /) = 3H +( - 5 < - 3 100 oJ = 6 i O B. y - 2 ^v - 6d = 6 + 2i = 8 ) - =3G 4 ^( p 3 6 9. Which of the following number lines shows the solution to the inequality given below ? x ^-4 3x 3- 3*< -15 OR 4x - 8H> x8 O . A O -1 0 -8 -6 -4 -2 0 2 4 O vv X [ 6 8 10 12 14 IG X > L| -2 0 2 4 6 8 10 12 14 o -4 -2 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 O -4 -2 I s * 10. Use elimination to find the solution to the system of equations. <9 ( 5* * *i j 1 li - + y 2x - 2y 5 = ( o>5 = 1 O c. = 1 O D. = O A. 9, y = =9) = 18 0 :• = -6 9 , y = -36 18 , y = 9 3, y . 11 The following system of equations is graphed below. 3* - 2y = -9 2 x + 2y = 4 j Find the solution to the system . . Q A x = - 1, y = 3 OB. i = 1, = 3 O C. * = l , = -3 OD. x = l, j> = 3 ^ - * - + 9 a x - p' i - ' z 1 9* V } 1 |0 )k - = 31 S > Sr . ¥ 12. Solve for x . = 6 x + 10 3 x - 5 =• 10 S a - 15 Sx - 5 OA. X OB.1 \ : 15 ~ 2 = 5 \ 5 O C. x ~ 7 i < > O D. 1 “ 15 14 » > \ : j ,- 3 i » . 13 Solve for y in the two equations below using substitution . + 3x = 12 XJy 108 A2 y = (o y 0 4. S O B. O y 4 y 8 O D. = $O 3 (,J 6) + - 10 8 & o + u3 y 10 S’ /3 y - 20 c. y V o 5 - - -y . 14 The following system of equations is graphed below. 2x 3 y = 6 2* + 4y = 22 - - - - Find the solution to the system. 5- 7 1 6 43 I V I 7 " i Z' -4 -5 J Q A. x = - L y = 2 t5 B-T= i7r = ~ ~ ^ o c. ro D. x = -!, >’ = -2 17. Solve for >» in the two equations below using substitution . O A. O c. y “ 2 y 1 4 o D. y ~ 3 - By = 2 2r +/ 6 y = 14 X- 4 v 2 JC 1 Ll 1 ( - /+ -4 V 18. Use elimination to find the solution to the system of equations. i \ 1 OA. = 4, y = 4 OB. = 0, y = 2 1 r* t -i OC.1 " x O D. = 4> V 8 2y 6y t + /4 N y = !I = 43 (o = 12 -38 r- ? ~ / 14 3 A v - io, y = 7 . 19 The following system of equations is graphed below. V 5 -5* - 4y = 7 -2* + 2y = 10 Find the solution to the system . O A. * = 2, y = -3 OBJ = -2J = 2 O C ^ = -3, y = 3 (Oj> )x = -3 , y = 2 « ^ 20. Rick and Casey are buying fish at the local market for their restaurants. Rick buys 3 brook trout for x dollars each and 3 rainbow trout fory dollars each and pays $90 for the fish . Casey buys 4 brook trout for x dollars each and 5 rainbow trout for y dollars each and pays $ 130 for the fish The system of equations shown below represents this situation. 3 C 1 ^ I9 H ( 3x + 3y = 90 ) . 3 (4x + 5y = 130) ' Which statement is true? — ' " ^ -3 . 0 - 10 r cn C A Casey paid $15 for each rainbow trout . r B Rick spent more money on rainbow trout than he did on brook trout. . itJ C C. Casey spent 3 times as much on brook trout than ho did on rainbow trout . C D. A brook trout costs $ 10 more than a rainbow trout. J > yd * - 'S'^ j ^ - 590 ^ 3x + 3 ^ (3C> (s> O 3X X " DO brccJ « ^ [TO L'vl daw gwra H ’' "U| y. W ' . 21 Which of the following number lines shows the solution to the compound inequality given below? -17 < 4* + 3 < 35 -jo -4 -2 i 2 4 6 O c. i O D. 8 10 12 0 2 4 6 8 10 12 14 -10 -8 -6 -4 -2 o 0 2 4 6 8 10 12 14 -10 -8 -6 -4 -2 0 10 12 14 o 2 4 6 8 22. Use elimination to find the solution to the system of equations. n (9a: + 2 y = 22 ) 63* + iH ) - 7V = -2 ) o B. x - O C. X ~ O D.1 2, y — 2 3x - 75 < ^ 37 y - 1 2' 3> y £. 14 -10 -8 -6 -4 -2 — * o o O B. i 0 -6 f £ lU / f^ -»5-LlH I \ * 50 ? ~ o 39 5 = 8, y = -1 23. Chloe is planning an event and purchasing floral arrangements. At Petals Plus, the arrangements cost $32.64 each, and the store charges $52.00 for delivery of the flowers to the event site. At Blooms, the arrangements cost $27.69 each, and the store charges $101.00 for delivery of the flowers to the event site . How many arrangements should she purchase from Blooms in order to get a better value? O B. 9 O C. 1O D. 8 39 4. H* -V ^ *+ 5 S) 97 53 y ioi v ? 9. g ^ k q x + i of I 'ALGEBRAvl — T - fi MODULE I' CONSTRUCTED-RESPONSE ITEM . 13 . John spends $94 to buy packages of cleaning supplies for a camp He buys t packages of towels; each package is $6 and contains 8 towels He also buys s packages of soap; each package is $ 4 and contains 10 bars of soap John buys 20 packages of cleaning supplies altogether. . . . A Write a system of two equations to represent the packages of cleaning supplies John buys. £4 f 4 4 5 = « 4- + 5 . = SO B. How many packages of towels does John buy? 5 = 3b - 4- Ir \ SO' 54 + s \ o-4 4 54 /4 - Go to the next page to finish question 13. Pennsylvania Keystone Algebra I Item and Scoring Sampler 2015 20 22 i 5 . kVa - . 13 - MODULE 4 i . Continued Please refer to the previous page for task explanation . . C Explain why it would not be possible for John to buy exactly 16 bars of soap i * * s ss 5 i l II £_or \ -VcJr6 k) e> air^ e jLfv\- 10> bars erP CTC * SOQ/S p KQJ/ L^ - VcA yield LOOU. I G> bars 6> ai_fp . a-P - ( 0> bars I UP \ odpa C UlO AeS b e_ i n be-Ucee U> OU\( - . ^ - c?C> 130,05 0 I Pennsylvania Keystone Algebra I Item and Scoring Sampler 2015 21 Constructed Response - Systems of Equations Here is a system of equations: -2x + 8y = 16 Q ( x - 4y = -O . A - . ; ’ y Q +g sA - § 7 . - CA ONCK A ^* -(o8 ~ (!) B . . Solve this system using the elimination method Show your work no Explain what your answer means -8 NicAae-S nncxUW ^ & v o£ LOCWA b tfVK no “ooluVionl . Solve this system using the graphing method —U THT ITy ~ 4 : i -4 t-H 1-H 4. — -4— _ ! L U + A ^^ * 51= 3j< ±ik - I i - t-- 1 " - 4-f .4 U4- — i ? * ; t i L T . 4 -V - H v = - -c / V - X Y —Y -• , no Vu-V' n ^^ & -s 2b =ftt^ - -\ ^3 - 0 npacxAVeV \ neo JLJ > . * = some. & tael crixplain how your graph from part B relates to your answer from part A. • rVe_ e ^ 'Wa-V 4ta_ Wo 6cxwo >\opl) k\(k cxocV AVe- Oeber <\Ve-TS <2.crV TxW 4 ' no O(AuMe>i0 j u6 ~V Wi5 ^ is -pV ' ^ ^ Aao^ ' ^ ^ .