Algebra 1
Mt 100
Chapter 9 Test
Name ______________________________
1. Show whether ( 4, − 2) is a solution to the system of equations " 3x − 4y = 20 . Your work
#
must support your conclusion.
$ 5x + 2y = 12
(8 points)
2. Determine whether the system of equations " 8x − 2 y = 6 has no solution or infinitely many
#
$ y − 4x = −3
solutions. Explain how you came to your conclusion. (8 points)
3. Use the figure to answer each of the following.
a) What is the slope of Line A? __________
b) What is the y-intercept of Line C? _________
c) Which lines form a system of equations with
a solution of (−3, 2) ? ______ and ______
d) Which lines form a system of equations that
has no solution? ______ and ______
e) What is the solution to the system formed by
lines A and C? _________
(2 points each)
4. Solve each system of equations using substitution or elimination.
a) " y = −2x − 3
#
$ 4x + 2y = 5
b) " 9x + 4y = 18
#
$ 5x − 2y = −28
c) "$
#
%$
1x−1 y =2
5
3
y+x=2
5. Solve the system of equations
using graphing.
" 3x + y = 5
#
$ 3x − 2 y = 8
(8 points)
(8 points each)
6. Graph the solution set for the system of inequalities.
(10 points)
# 2x + y ≥ −1
$
% x− y<5
7. The graph shows the solution to the system of inequalities # 5x + 3y ≥ 15 .
$
(2 points each)
% 2x − 2y < 6
a) Name a point that is a solution to the
system. _______________
b) Name a point that is a solution to
! 2x − 2y < 6 , but not a solution to
5x + 3y ≥ 15 . _______________
c) Which inequality is (3, 0) a solution
to? _________________________
d) Yes or No; the origin is a solution to
this system of inequalities. __________
Write a system of equations and solve problems 8-10.
8. The sum of two numbers is 16. Their difference is 4. What are the two numbers?
(8 points)
9. Mitchell owes $13,250 on two student loans. One loan has an APR of 5%; the other, an APR
of 8%. If the total interest after one year is $727, what is the amount of each loan?
(8 points)
10. An airplane travels 2400 Km in 4 hours flying with the wind. The return trip takes 5 hours.
Find the rate of the plane in still air and the rate of the wind.
(8 points)