1. Systems of Linear Equations
Chapter 7
Systems of Linear Equations

2. 1. Which linear system has the solution x = 3 and y = -1?
a) 2x + 3y = 3 b) 4x – 2y = 14
x + y = x + y = 7
c) 2x – 3y = 3 d) 2x – 3y = 9
-x + 6y = x + 6y = -9
2(3) + 3(-1) = 3
3 + (-1) = 4
4(3) – 2(-1) = 14
2(3) + (-1) = 7
6 – 3 = 3
= 14
6 – 1 = 7
3 = 3
14 = 14
2(3) – 3(-1) = 9
-3 + 6(-1) = -9
2(3) – 3(-1) = 3
-3 + (-6) = -9
6 + 3 = 9
6 – (-3) = 3
-9 = -9
9 = 9

3. 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 = 228
x – 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.
79 – 35 = 44
2(79) + 2(35) = 228
44 = 44
= 228
228 = 228

4. (5, -3) 1 y = mx + b 2 1 2 3. Solve this linear system by graphing.
2x + y = 7
3x + 3y = 6 1
y = mx + b 2 1
2x + y = 7
-2x x
y = -2x +7 2
3x + 3y = 6
-3x x
3y = -3x + 6
(5, -3)
x = 5 y = -3
y = -x + 2

5. 4. Determine the number of solutions to the linear system
-6x + 2y = -4
3x – y = 2 1
DO NOT SOLVE FOR X AND Y 2
Compare slope and y-intercept:
1 – If m and b are the same  Infinite Solutions
2 – If only m is the same  No Solutions
3 – If m and b are different  One Solution
y = mx + b 1
-6x + 2y = -4
+6x x 2
3x – y = 2
2y = 6x – 4
-3x x
Infinite Solutions
-y = -3x + 2
y = 3x – 2
y = 3x – 2
m = 3
b = -2
m = 3
b = -2

6. 5. Solve the following system using both Substitution and Elimination 1 2
Get rid of fractions! 1
4( ) 2
3( )

7. 5. (part 2) Solve the following system using
both Substitution and elimination 1 2
Substitution: 2 1
-6y -6y

8. 5. (part 3) Solve the following system using
both Substitution and elimination 1 2
Elimination:
6( ) 2

9. Solve the following system using both Substitution and elimination
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
Create system of linear equations 1
let a = number of marks on part A
b = number of marks on part B 2

10. Part A is out of 50, Part B is out of 25
6. (part 2) Solve the following system using
both Substitution and elimination 1 2
Substitution: 1 2
-b -b
Part A is out of 50, Part B is out of 25

11. 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 2
Elimination:
0.8( ) 1
Part A is out of 50, Part B is out of 25