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96test1ans - Math 96 — Test 1 Name ANSU 5 KS Show work...

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Unformatted text preview: September 20, 2011 Math 96 — Test 1 Name ANSU 5 KS Show work for full credit. 1. Determine whether the ordered pair (x, y) = (3,5) satisfies the system {9x = 3y + 12, am % 3033*)2 4=3x—y. 2'} ; 1€+ 1’2, T ‘F L] —: 3C5\_ S K 6'5 , (3) S) Sqi'is "5-3 1L4 Sysifw‘. J Li 1 ‘15 2. Determine whether (x, y,z) = (2,—1,—2) satisfies the system x + y — 2z = 5, - ~ 2x '— y — z = 7, ‘ — -'2. : — + - t) J (EV-L” [2&3 2 I L‘— —x—2y+3z=6. NA —Q—I\— g—2\ = L1+1+2=7 J ~LZ\—LQ-‘\+Bt-2\=—z+2—<p a 497m, iNO i ,, (2., *1, 4,) dacyfi‘ $64.sz 4% AMA Qquct‘hd’x . ' x + 4 = —2 3. Solve by graphing { y 5 . That is, graph the two lines and find the point (x,y) where y = —x — the lines intersect. 2x—2y=6 y—x=5 .Nb Sail/hi)“ i Q (\mASIgi'ud’ 375% V\\ 4. Solve by graphing { September 20,2011 . Math 96 - Test 1 page 2 of 4 Soho. b-/ (NL- SuMS'Tfiu‘hM Maker! 5. y 2x 9 ‘6. x=20—2y {x+3y=8 {2x+4y=—24 , 2120a §+47=’?—"' K-FBOZX" c?» 8 140-4]; +qy:_z_&+ x+®x- ~2? -3 Hoz—ZH WW yzzes- ER Solve by the elimination method. 7. x—2y=6 8. U) 3x+4yl=25 {—x+3y=—4 Q {2X+y=10 7:1 ~ [M Q)? 31 x + ‘47 :25 x-%&=V —— _ . ~ - x —'-l — ”O xngb ‘4©. 8 v Kilo -—§x : —IS @ Mg, Solve the system of equations. 9L!) x+3y+2z=14, K3X+Y =/O © y+52=21, (9+7 :/() Q5 —y—4z=—n, y: H tbfiE‘ 2: H 7+563= ' 012A 7+1 ’ 7=’ ‘X+3>(I\+?i‘1\:‘q K+$+81H sz VWYIE):(B,7.Q) 10. A warehouse contains parts to manufacture unicycles, bicycles, and tricycles. There are 23 seats, 51 wheels, and 20 sets of handlebars. How many unicycles, bicycles, and tricycles can be manufactured from these parts? kcj— x: number; ohm/€195 7-; M). 3'? b‘CXQ—b-K J E: MO. 5? $6,7le \D 320331 X 4r \/ + Z :1 {2,5 7+X:ZD -.> 7/:(2. @ u \s: x Jr Z7 4— 52 : 5! x+12+8z2532<$3 (E) kavAkBVS'. 7/ + 32-. Z 2.0 ““(D‘I'QD : ED. 1 + a? 1 18 z = % +6) +62%): September 20, 2011 Math 96 - Test 1 page 3 of 4 Solve. ‘ 11. [2x+3|=5 12. |x—2|=|2x—7| Zx+°>=9 0" 9—‘91'33‘5 x——Z:2x—7 04‘ >02?- -(Zx~7) ZX:.Z 0? 2K 75"? X-LLSZZK (I? X_Z:~2x+7 x11] or‘ )E on X :-2_x+‘i or 3x20] Solve. Either graph the solution or write the answer using interval notation. 13. l2x—6ls4 14. lx—4|>2. on e ”bees—LI x4, >1 0“ xew<~2 Lézxglo X>(o or x<’2. 1 e x é 5‘ (MM—W E g H% 31% 2. (a X 1- 5 ig.oo,e)u((o,oo\) MM 15. Graph the system of inequalities @ x — y 2 2, Find coordinates of vertices formed. @ x+ys4, September 20, 2011 Math 96 - Test 1 page 4 of 4 16. a. Write the matrix that represents the system ' x + 5 y = 14. I '5 m 3x - 4y = 4 3 —H H b. Perform the row operation, —3R1 + R2, on the second row of the matrix and write the new matrlx. // S “‘1 (3 - I ‘1 e 3 8 c. Perform the row operation, —LR2, on the second row of the resulting matrix. 19 4 5 )4 o 1 a d. Write the system of equations equivalent to the matrix that results from c, then solve the s stem. _ y X+Sy=1Li .9 ><+5m—H _ a X + ID = “-1 y — x : Ll ®#B=Mtt)l L! 17. Write a matrix to represent the system 2x — 4y + z = 3 , but do not solve the system. —3x+7y—%z= —1 2_ -‘-l ’1 3 y - z = 0 ~3 'r'fi 4 o 1 «i O (a 18. A system of equations in x, y, and z is represented by the matrix 1 —2 3 9 . Solve the 0 1 3 5 X — + :. 2'7! 32 0’ 0 0 '1 2 system of equations. 7 9' 31 : 5 z=£ )1 + 74% = 5 y+b1§ 7=~i my, at“ J1, 25) X’ZL‘1X4—5C233? X+Z+bL7 x+8=9 )k:l ...
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