SELF CHECK! Make sure you are prepared for this test!STUDY!

m = — ( 3, 4 ) y = mx + b

m = — ( 4, 1 ) y = mx + b

one solution no solution infinite solutions ANY 2 lines that cross (intersect) at one point. ANY 2 lines that are parallel (never intersect). ANY 2 lines that are the exact same line!

If one equation in a system was y = x + 3, the “solution to a system” must be a point on that line! (must make the equation TRUE) Complete the ordered pairs: ( 5, ___ ) ( 2, ___ ) ( 1, ___ ) ( –3, ___ ) ( 4, ___ ) ( 3, ___ ) ( 0, ___ ) ( –5, ___ ) y = –2

“is” is the EQUAL SIGN! = b + g = less than means subtract 10. – 10 “twice the # of girls… 2g Total of 29 students… Add boys & girls. “The # of boys is…” b = ( ) ( 2g – 10 ) + g = 29 3g – 10 = g = 39 g = girls Use the 1st equation: b = 2g – 10 b = 2(13) – – 10 b = boys

( ) –2 ( 7 – 2y ) + 3y = 14 Dist. Prop. – y + 3y = 14 C.L.T. – y = y = 28 y = 4 Use the 2nd equation: x = 7 – 2y x = 7 – 2(4) 7 – 8 x = – 1 (, ) – 1 4 Since one equation has a variable by itself… SUBSTITUTION.

( ) (– 1) 3x + 8y = 14 –3x + 4y = – 2 12y = 12 y = 1 Use either equation: 3x – 4y = 2 3x – 4(1) = 2 3x – 4 = x = 6 x = 2 (, ) 2 1 Both standard form… use elimination!

19 people… add adults and students a + s = 19 “5 hours” is EXTRA INFO! adults cost $9 9a students cost $4 4s everyone cost $111 + = 111 () ( ) (-4) – 4a – 4s = – 76 9a + 4s = 111 5a = 35 a = 7 7 adults The 1st equation looks easier: a + s = s = 19 –7 – 7 s = students Both standard form… use elimination!

3 / 2 (-6) – 9 = – 18 3 / 2 (-3) – 9 = – / 2 (0) – 9 = – 9 3 / 2 (3) – 9 = – / 2 (6) – 9 = 0 – 4 / 3 (-6) + 8 = 16 – 4 / 3 (-3) + 8 = 12 – 4 / 3 (0) + 8 = 8 – 4 / 3 (3) + 8 = 4 – 4 / 3 (6) + 8 = 0 Which ordered pair is the SAME in both tables? ( 6, 0)

( ) 4x – ( 2x – 5 ) = 7 Dist. Property 4x – 2x + 5 = 7 C.L.T. 2x + 5 = 7 – 5 – 5 2x = 2 x = 1 Use the 1st equation: y = 2x – 5 y = 2(1) – 5 2 – 5 y = – 3 (, ) 1 – 3 Since one equation has a variable by itself… SUBSTITUTION.

– 6x = – 54 x = 9 Use either equation: – 2x + 8y = – 26 – 2(9) + 8y = – 26 – y = – y = – 8 y = – 1 (, ) 9 – 1 Both standard form… use elimination!

( ) 1 + x = 2x + 6 – 2x – 2x 1 – x = 6 – 1 – 1 – x = 5 x = – 5 Choose either equation: y = 1 + x y = 1 + (–5) y = – 4 (, ) – 5 – 4 – 4– 4 Since one equation has a variable by itself… SUBSTITUTION.

add nickels & dimes n + d 103 coins = 103 nickels are worth 0.05 ea. 0.05n dimes are worth 0.10 ea. 0.10d All the coins are worth $ = 8.00 The problem says to write the system… NOT SOLVE IT!

Let c be packs of cards… and let t be tattoos. Jose  4c + 3t Jose spent $11.45= L.C.  1c + 4t L.C. spent $9.85= 9.85 () ( ) (– 4) 4c + 3t = – 4c – 16t = –39.40 – 13t = –27.95 t = 2.15 $2.15 per tattoo Use one of the equations: c + 4t = 9.85 c + 4(2.15) = 9.85 c = 9.85 – 8.60 c = 1.25 $1.25 per pack of cards Both standard form… use elimination!

() ( ) (–2) 2a + 2b = 16 –2a – 2b = 16 0 = 32 True? NO! No Solution Both standard form… use elimination!

How many less? (subtract) 30 – Animals total? (add) How many times? (divide) 30 ÷ 10 3

(, ) 4 3

Failure to prepare means you must be prepared to fail.STUDY!