Download Lesson 7

99
Algebra 1 Review for Chapter 7 (And 6.7)
Solving by Graphing: Graph each equation and find the point of intersection. That is the solution
to the system.
1. y =
2
x 1
3
y = -x + 4
2. y = -2
2x - 5y = 10
Solving by Substitution: Isolate one variable and plug that into the other equation. Then solve
for the variable that is left. Then plug that value into either original equation and solve for the
second variable.
3. x = 3 – 2y
2x + 6y = -12
4. 3x + y = -5
x – 2y = 3
Solving by Combination: Eliminate one of the variables so that you can solve for the remaining
variable. You may have to multiply through one or both equations by a number.
5. x + 3y = 7
-x + y = -3
6. x + 3y = 4
2x – y = 8
If you solve the system and get:
 x = a number and y = a number then there is one solution and you write it as an ordered pair.
(Remember…these are the type of problems we have been working with.) If you graph both
you will have two different lines that intersect at one point (the solution).
7. 3x – y = -9
3x + 5y = -15
 a true statement such as 0 = 0 or 3 = 3 or –4 = -4, then you have many solutions and you need
to write “many solutions”. If you graph both you will end up with the same line.
8. -9x + 9y = 18
3x – 3y = -6
 a false statement such as 0 = 4 or 2 = -5, then you have no solutions and you need to write “no
solutions”. If you graph both you will end up with two parallel lines.
9. 3x – 4y = -12
y=
3
x–3
4
Graphing Linear Inequalities
Think about what type of line to use and where to shade the inequality.
10.) y > ½x + 3
11.) 2x - 3y < -6
Identifying Solutions to a System of Inequalities:
Tell whether the ordered pair is a solution to the system of inequalities. (Circle your answer.)
12.
13.
14.
Yes- it is a solution
Yes- it is a solution
Yes- it is a solution
No - it is not a solution
No - it is not a solution
No - it is not a solution
Graph the system of inequalities.
15.
17.
19.
y  2x  3
y  x 1
x0
yx
y  2x  3
y  2x  4
16.
18.
20.
x 1
2 x  3 y  6
x  y  3
y  2x 1
y  x3
2 y  x  4
Chapter 7 Review Homework
100
Solve the Linear System by Graphing
1.
3 x  y  6
2.
x y 2
Solve the Linear System by Substitution
3.
5.
y  5x  7
4.
4 x  y  1
3x  y  19
6.
x y 7
2 x  y  5
x  y  1
x  y  11
x  3y  1
15 x  y  70
3 x  2 y  8
Solve the Linear System by Elimination (Combination)
7.
8 x  3 y  9
8 x  y  29
8.
x  5 y  3
3 x  5 y  11
9.
4 x  y  17
7 y  4x  9
Tell whether the linear system has one solution, no solutions or many solutions.
10.
15 x  3 y  12
y  5x  4
11.
4 x  y  4
12.
8 x  2 y  2
Graph the Linear Inequality
13. y  6
14. y  2 x  5
Graph the System of Linear Inequalities
15.
17.
y  2x  2
y  x 1
x y 6
x y 2
16.
18.
y  3x  2
y  x4
y  2
2 x  3 y  6
12 x  3 y  18
4 x  y  6