Unit 6 Systems of Equations
Study Guide
LT-1: one solution, no solution and many solution
1) put both equations into slope-intercept form y = mx + b
2) Look at slopes
 If slopes are different can ONLY be one solution
 If slopes were the same then look at y-intercepts
 If y-intercepts are different then no solution…lines are
parallel
 If y-intercepts are the same then many solutions…..lines are
the same line.
Determine if each system has one solution, no solution, or many
solutions.
1. y = 3x + 14
Y = -3x + 14
2. 5y = x – 9
4x – 10y = 18
3. 3x + 2y = 7
27x + 18y = 5
4. x + 5y = 0
5. 8x + 10y = 21
6. Y = 1.9x =6
25y = -5x
7. 20y = 35x + 90
12y = 21x + 54
4
5
y = - x + 24
8. 27x + 39y = 186
-18x -26y = -124
3y = 5.7x – 18
9. -16x +56y = 184
12x – 42y = -132
LT-2/ LT-3: Are one solution systems crossing at ONLY one point.
You will graph these systems on the same graph
1) Get both equations into slope-intercept form y = mx + b
2) Locate your y-intercept (b) on the graph.
3) Locate your slope (m) in your equation and start from your yintercept using your
rise
.
run
4) Make at least 3 points to make your line.
Solve by graphing. Put on your own graph paper.
1. x + y = 4
2x – y = 5
2. X + y = 0
3x – 2y = 10
3. 2x + y = 7
x+y=3
4. x + y = 1
2x – 2y = 6
5. 3x + 2y = 9
4x – y = 1
6. 3x – 4y = -4
6x – 2y = 1
LT-4: You are using substitution, addition and subtraction to solve
these problems. There is a file under unit 6 that has an explanation of
these 3 in detail.
Addition Method
1. x + y = 10
X–y=2
2. 2x – 5y = -19
3x + 2y = 0
3. X + 5y = -13
2x – 5y = -19
4. 2x – y = -6
2x + 3y = 14
5. X + 2y = -1
4x + 3y = -9
6. 2x – 3y = 6
x + 3y = 12
Subtraction Method
1. 5x – 2y = 3
5x + y = -9
2. 2x – y = -6
2x + 3y = 14
3. X – 3y = -13
-x + 4y = 15
4. 2x + 2y = -8
3x – 3y = 18
5. 4x + 2y = 2
5x + 2y = 4
6. 3x + 4y = 22
x – 5y = -37
Substitution Method
1. y = 2x
2x + y = -12
2. Y = x + 3
3x + y = 11
3. 2x – 3y = -25
3x + y = 1
4. x + y = 3
4x – 2y = 18
5. X – y = 4
2x – 3y = 6
6. 3x + 4y = 22
x – 5y = -37