Review 3-1
and 3-2
SLIDE SHOW
3 x + 4y  – 4
Solve
the
linear
system
using
1.
x + 2y  2
the substitution method.
SOLUTION
Equation 1
Equation 2
x + 2y  2
x  – 2y + 2
3(– 2y + 2) + 4y  – 4
-6y+6+4y  – 4
-2y = -10
x  – 2y + 2
x  – 2(5) + 2
x  –8
y5
The solution is (– 8, 5).
Solve the linear system using
2. the substitution method.
x – 2y  3
2x – 4y  7
x2y+3
2(2y + 3) – 4 y  7
67
Because the statement 6 = 7 is never true, there is no solution.
Solve the linear system using the
3. linear combination/elimination method.
2 x – 4y  13
4 x – 5y  8
Equation 1
Equation 2
SOLUTION
Multiply the first equation by – 2 so that x-coefficients differ only in
sign.
2 x – 4y  13
4 x – 5y  8
•
–2
– 4x + 8y  – 26
4 x – 5y  8
3y  –18
y  –6
The Linear Combination Method: Multiplying One Equation
2 x – 4y  13
4 x – 5y  8
Solve the linear system using the
linear combination method.
Add the revised equations and solve for y.
Equation 1
Equation 2
y  –6
Substitute the value of y into one of the original equations.
2 x – 4y  13
Write Equation 1.
2 x – 4(– 6)  13
Substitute – 6 for y.
2 x + 24  13
x–
(-
The solution is
–5
Simplify.
11
2
1
, –6
2
Solve for x.
).
4.
6 x – 10 y  12
– 15 x + 25y  – 30
Solve the linear system
SOLUTION
Since no coefficient is 1 or –1, use the linear combination
method.
6 x – 10 y  12
•
5
30 x – 50 y  60
– 15 x + 25 y  – 30 •
2
– 30 x + 50 y  –60
Add the revised equations.
00
Because the equation 0 = 0 is always true, there are
infinitely many solutions.
5.
Solve the linear system using the
linear combination method.
7 x – 12 y  – 22
– 5 x + 8 y  14
Equation 1
Equation 2
SOLUTION
Multiply the first equation by 2 and the second equation by 3
so that the coefficients of y differ only in sign.
7 x – 12 y  – 22 •
2
14 x – 24y  – 44
– 5 x + 8 y  14
3
– 15 x + 24y  42
•
Add the revised equations and
solve for x.
–x  –2
x 2
Solve the linear system using the
linear combination method.
7 x – 12 y  – 22
– 5 x + 8 y  14
Add the revised equations and solve for x.
Equation 1
Equation 2
x2
Substitute the value of x into one of the original equations.
Solve for y.
– 5 x + 8 y  14
– 5 (2) + 8y  14
y=3
Write Equation 2.
Substitute 2 for x.
Solve for y.
The solution is (2, 3). Check the solution algebraically or graphically.
6. If Brian bought 6 markers and 12 pens for
$21.60 and then had to go back and buy 18 more
markers and 20 pens for $50.40. How much was
x = 1.8
each item?
6x + 12y = 21.60
18x + 20y = 50.40
y = .9
Markers costs $1.80
Pens costs $0.90
7. If Maria bought 33 books notebooks for $393.
Each book costs $23.50 and each notebook costs
$2.25. How many of each did she purchase?
x + y = 33
23.5x + 2.25y = 393
x = 15
y = 18
15 Books
18 Notebooks
Homework
Textbook
Page 155 Quiz 1
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