chapter 7 systems of linear equations. a) 2x + 3y = 3 b) 4x – 2y = 14 x + y = 4 2x + y = 7 c) 2x...
TRANSCRIPT
Chapter 7
Systems of Linear Equations
a) 2x + 3y = 3 b) 4x – 2y = 14 x + y = 4 2x + y = 7
c) 2x – 3y = 3 d) 2x – 3y = 9 -x + 6y = -3 -x + 6y = -9
1. Which linear system has the solution x = 3 and y = -1?
3 + (-1) = 4 4(3) – 2(-1) = 14
12 + 2 = 14
2(3) + 3(-1) = 3 6 – 3 = 3
2(3) – 3(-1) = 3
6 – (-3) = 3
2(3) – 3(-1) = 9
9 = 9
6 + 3 = 9
-3 + 6(-1) = -9
-9 = -9
-3 + (-6) = -9
3 = 3 14 = 14
2(3) + (-1) = 7 6 – 1 = 7
2. a) Create a linear system to model this situation.
2 jackets and 2 sweaters cost $228. A jacket costs $44 more than a sweater
Cost jackets = x Cost sweaters = y
2x + 2y = 228x – y = 44
b) Kurt has determined that a sweater costs $35 and jackets cost $79. Use the linear system from part a to verify that he is correct.
2(79) + 2(35) = 228158 + 70 = 228
228 = 228
79 – 35 = 4444 = 44
3. Solve this linear system by graphing.2x + y = 73x + 3y = 6
y = mx + b12
1 2x + y = 7-2x -2x
y = -2x +7
2 3x + 3y = 6-3x -3x
3y = -3x + 63 3 3 y = -x + 2
(5, -3) x = 5 y = -3
4. Determine the number of solutions to the linear system-6x + 2y = -4 3x – y = 2
DO NOT SOLVE FOR X AND Y
Compare slope and y-intercept:
1 – If m and b are the same Infinite Solutions2 – If only m is the same No Solutions3 – If m and b are different One Solution
y = mx + b
12
1 -6x + 2y = -4+6x +6x
2y = 6x – 42 2 2
y = 3x – 2
m = 3 b = -2
2 3x – y = 2-3x -3x
-y = -3x + 2-1 -1 -1
y = 3x – 2 m = 3 b = -2
Infinite Solutions
5. Solve the following system using both Substitution and Elimination
244
33 yx
1223
2 yx
Get rid of fractions!
1
2
244
33 yx1 4( )
96312 yx
1223
2 yx2 3( )
3662 yx
5. (part 2) Solve the following system using both Substitution and elimination 1
2
3662 yx2-6y -6y
96312 yx
3662 yx2 2 2
3662 yxSubstitution:
183 yx
96312 yx1963)183(12 yy
y36 216 y3 96
y39 96216
31239 y3939 8y
18)8(3 x1824 x6x
216216
5. (part 3) Solve the following system using both Substitution and elimination 1
2
3662 yx6( )
96312 yx
x12
3662 yxElimination:
0 y39 312
8y
96312 yx
y36 216
-39 -39
2 3662 yx
36482 x4848
122 x 2 2
6x
36)8(62 x
6. Sam scored 80% on part of A of a math test and 92% on part B of the math test. His total mark for the test was 63. The total mark possible for the test was 75. How many marks is each part worth?
Solve the following system using both Substitution and elimination
75ba
6392.08.0 ba
Create system of linear equations
1
2
let a = number of marks on part A b = number of marks on part B
6. (part 2) Solve the following system using both Substitution and elimination 1
2
75ba1-b -b
ba 75
Substitution:
6392.08.0 ba26392.0)75(8.0 bb
60 b8.0 b92.0 63
60 6312.0 b
312.0 b12.012.0
25b
2575 a
50a
6060
75ba6392.08.0 ba
Part A is out of 50, Part B is out of 25
6. (part 3) Solve the following system using both Substitution and elimination 1
275ba0.8( )
a8.0
Elimination:
0 b12.0 3
25b
6392.08.0 ba
b8.0 60
0.12 0.12
1 75ba
7525a2525 50a
75ba6392.08.0 ba
Part A is out of 50, Part B is out of 25