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Warm-Up Exercises
Solve the linear system.
1. 4x – 3y = 15
2x – 3y = 9
ANSWER
(3, –1)
2. –2x + y = –8
2x – 2y = 8
ANSWER
(4, 0)
Warm-Up Exercises
3. You can row a canoe 10 miles upstream in 2.5 hours
and 10 miles downstream in 2 hours. What is the
average speed of the canoe in still water?
ANSWER
4.5 mi/h
Warm-Up1Exercises
EXAMPLE
Multiply one equation, then add
Solve the linear system:
6x + 5y = 19
Equation 1
2x + 3y = 5
Equation 2
SOLUTION
STEP 1 Multiply Equation 2 by –3 so that the
coefficients of x are opposites.
6x + 5y = 19
2x + 3y = 5
STEP 2 Add the equations.
6x + 5y = 19
–6x – 9y = –15
–4y = 4
Warm-Up1Exercises
EXAMPLE
Multiply one equation, then add
STEP 3 Solve for y.
y = –1
STEP 4 Substitute –1 for y in either of the original
equations and solve for x.
2x + 3y = 5
2x + 3(–1) = 5
2x + (–3) = 5
2x = 8
x=4
Write Equation 2.
Substitute –1 for y.
Multiply.
Subtract –3 from each side.
Divide each side by 2.
Warm-Up1Exercises
EXAMPLE
Multiply one equation, then add
ANSWER
The solution is (4, –1).
CHECK Substitute 4 for x and –1 for y in each of the
original equations.
Equation 1
Equation 2
6x + 5y = 19
2x + 3y = 5
?
?
6(4) + 5(–1) = 19
2(4) + 3(–1) = 5
19 = 19
5=5
Warm-Up2Exercises
EXAMPLE
Multiply both equations, then subtract
Solve the linear system:
4x + 5y = 35
Equation 1
2y = 3x – 9
Equation 2
SOLUTION
STEP 1
Arrange the equations so that like terms are in
columns.
4x + 5y = 35
–3x + 2y = –9
Write Equation 1.
Rewrite Equation 2.
Warm-Up2Exercises
EXAMPLE
Multiply both equations, then subtract
STEP 2
Multiply Equation 1 by 2 and Equation 2 by 5 so that
the coefficient of y in each equation is the least
common multiple of 5 and 2, or 10.
4x + 5y = 35
8x + 10y = 70
–3x + 2y = –9
–15x +10y = –45
STEP 3
Subtract the equations.
STEP 4
Solve for x.
23x
= 115
x=5
Warm-Up2Exercises
EXAMPLE
Multiply both equations, then subtract
STEP 5
Substitute 5 for x in either of the original equations
and solve for y.
4x + 5y = 35
Write Equation 1.
4(5) + 5y = 35
Substitute 5 for x.
y=3
ANSWER
Solve for y.
The solution is (5, 3).
Warm-Up2Exercises
EXAMPLE
Multiply both equations, then subtract
Substitute 5 for x and 3 for y in each of the
original equations.
CHECK
Equation 1
Equation 2
4x + 5y = 35
2y = 3x – 9
?
4(5) + 5(3) = 35
2(3) = 3(5) – 9
35 = 35
ANSWER
?
The solution is (5, 3).
6=6
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Solve the linear system using elimination.
1.
6x – 2y = 1
–2x + 3y = –5
ANSWER
The solution is (–0.5, –2).
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Solve the linear system using elimination.
2.
2x + 5y = 3
3x + 10y = –3
ANSWER
The solution is (9, –3).
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Solve the linear system using elimination.
3. 3x – 7y = 5
9y = 5x + 5
ANSWER
The solution is (–10, –5).
EXAMPLE
Warm-Up3Exercises
Standardized Test Practice
Darlene is making a quilt that has alternating stripes of
regular quilting fabric and sateen fabric. She spends
$76 on a total of 16 yards of the two fabrics at a fabric
store. Which system of equations can be used to find
the amount x (in yards) of regular quilting fabric and
the amount y (in yards) of sateen fabric she
purchased?
A x + y = 16
x + y = 76
C x + y = 76
4x + 6y = 16
B x + y = 16
4x + 6y = 76
D x + y = 16
6x + 4y = 76
EXAMPLE
Warm-Up3Exercises
Standardized Test Practice
SOLUTION
Write a system of equations where x is the number of
yards of regular quilting fabric purchased and y is the
number of yards of sateen fabric purchased.
Equation 1: Amount of fabric
x
+
y
=
16
EXAMPLE
Warm-Up3Exercises
Standardized Test Practice
Equation 2: Cost of fabric
4
x
+
y
6
The system of equations is:
x + y = 16
4x + 6y = 76
=
76
Equation 1
Equation 2
ANSWER
The correct answer is B.
A
B
C
D
Warm-Up
Exercises
GUIDED
PRACTICE
4.
for Example 3
SOCCER A sports equipment store is having a sale
on soccer balls. A soccer coach purchases 10
soccer balls and 2 soccer ball bags for $155. Another
soccer coach purchases 12 soccer balls and 3
soccer ball bags for $189. Find the cost of a soccer
ball and the cost of a soccer ball bag.
ANSWER
soccer ball $14.50, soccer ball bag: $5
Warm-Up Exercises
Warm-up:
Homework: Page 396 #2-32 even #33 #37 #38
and #39
Daily
Homework
Quiz
Warm-Up
Exercises
Solve the linear system using elimination.
1.
8x + 3y = 12
–2x + y = 4
ANSWER
2.
(0, 4)
–3x + 2y = 7
5x – 4y = –15
ANSWER
3.
(1, 5)
–7x – 3y = 11
4x = 2y+ 16
ANSWER
(1, –6)
Daily
Homework
Quiz
Warm-Up
Exercises
4. A recreation center charges nonmembers $3 to use
the pool and $5 to use the basketball courts. A
person pays $42 to use the recreation facilities 12
times. How many times did the person use the
pool?
ANSWER
9 times