Applying Systems of
Equations – Part 2
Honors Math – Grade 8
1
Define the
Variables
Let x = the first number and
y = the second number.
1. Write the equations in column form. Multiply
to eliminate a variable.
Distribute on
both sides of
=
The numbers are 2 and -5.
Seven times a number plus three
times another number is negative one.
The sum of the two numbers equals
negative three. What are the
numbers?
Write a
system of
equations.
Seven times a number plus
three times another is -1.
7x + 3y = -1
The sum of the two numbers is
-3.
x + y = -3
7 x  3 y  1

 x  y  3
2
Define the
Variables
Let a = the first mutual fund & b
= the second mutual fund
1. Write the equations in column form. Multiply
to eliminate a variable.
Mariah invested $25,000 in two mutual funds.
One of the funds rose 5% in one year, and the
other rose 9% in one year. If Mariah’s
investment gained a total of $1770 in one year,
how much did she invest in each mutual fund?
Write a
system of
equations.
The total investment is 25000.
a + b = 25000
The interest gained is 1640.
.05a + .09b = 1770
I = prt
a  b  25000


.05a  .09b  1770
Solve the equation
Mariah invested $12,000 @
5% and $13,000 @ 9%.
3
Define the
Variables
Let n = the cost of a notebook
and p = the cost of a pen.
1. Write the equations in column form. Multiply
to eliminate a variable.
Distribute
2. Since the coefficients of
n are 12 & 12 (the same),
subtract the equations.
3. Now substitute p = 2 in either equation and solve.
A pen costs $2 and a
notebook costs $2.50.
The cost of four notebooks and five
pens is $20. The cost of six
notebooks and two pens is $19. How
much does each notebook and pen
cost?
Write a
system of
equations.
4 notebooks and 5 pens = 20
4n + 5p = 20
6 notebooks and 2 pens = 19.
6n + 2p = 19
4n  5 p  20

 6n  2 p  19
Solve the equation
4
Define the
Variables
Let b = the rate of the barge in still
water and c = the rate of the
current.
1. Write the equations in column form; multiply.
Distribute
A coal barge on the Ohio River
travels 24 miles upstream in 3
hours. The return trip takes the
barge only 2 hours. Find the rate
of the barge in still water.
r
t
d
Down b + c 2 24 2(b + c) = 24
Up
b – c 3 24 3(b – c) = 24
Write a
system of
equations.
2b  2c  24

3b  3c  24
2. Since the coefficients of
c are opposites, ADD the
equations.
The rate of the barge in still
water is 10 miles per hour.
d=rt
Solve the equation
The c variable is
eliminated
because -6 + 6 = 0
5
Define the
Variables
Let b = the rate of the canoe in still
water and c = the rate of the
current.
1. Write the equations in column form; multiply.
Distribute
A canoe travels 4 miles upstream
in one hour. The return trip takes
the canoe 1.5 hours. Find the
rate of the canoe in still water.
r
t
d
Down b - c 1.5 4 1.5(b + c) =4
Up
b+c
Write a
system of
equations.
1
4
The rate of the canoe in still
water is 10/3 miles per hour.
1(b – c) = 4
1.5b  1.5c  4

bc  4

2. Since the coefficients of
c are opposites, ADD the
equations.
d=rt
Solve the equation
The c variable is
eliminated
because
-1.5 + 1.5 = 0