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Mr. Sims
Solve by substitution.
1. 4x – 3y = 3
get one equation to
read x = or y =
x – 2y = -8
+2y
Algebra 2
Section 10.6
Review for Test
x = 2y - 8
+2y
4(2y – 8) – 3y = 3
8y – 32 – 3y = 3 distributive property
5y – 32 = 3 combine like terms
+32 +32
5y = 35
y=7
substitute into equation
that reads x =
x = 2y – 8
x = 2(7) – 8
x = 14 – 8
x=6
Mr. Sims
Solve by addition.
2. -3 2x + 3y = 10
2 3x + 5y = 19
multiply either top, bottom, or both
by a term, so that, when added
a variable cancels out
-6x – 9y = -30
6x + 10y = 38
y = 8 substitute into any
equation with x and y
2x + 3y = 10
2x + 3(8) = 10
2x + 24 = 10
-24 -24
2x = -14
x = -7
Mr. Sims
Solve the system of equations.
3. 2x – 3y + 5z = 13
-3x + 3y – 2z = -8
5x – 2y + 4z = 2
3.) use the two new equations
to solve for a variable
11 -x + 3z = 5
11x + 2z = -20
-11x + 33z = 55
11x + 2z = -20
35z = 35
z=1
1.) choose two equations
and eliminate one variable
2x – 3y + 5z = 13
-3x + 3y – 2z = -8
4.) keep substituting until
all variables are solved for
-x + 3z = 5
substitute 1 in for z, into any
equation containing z and
one other variable
2.) choose two different
equations and eliminate
the same variable {y}
-2 2x – 3y + 5z = 13
3 5x – 2y + 4z = 2
- 4x + 6y – 10z = -26
15x – 6y + 12z = 6
11x + 2z = -20
2x – 3y + 5z = 13
2(-2) – 3y + 5(1) = 13
-3y = 12
- 4 – 3y + 5 = 13
y=-4
-3y + 1 = 13
11x + 2z = -20
11x + 2(1) = -20
11x + 2 = -20
-2
-2
11x = -22
x = -2
substitute 1 in for z and -2 in for x
into any equation with x,y, and z
Mr. Sims
Find the value of each determinant.
4.
3
4
6
-2
= -3(-2) – 6(4)
= 6 – 24
= -18
5.
ab
2a  b
b
ab
= (a + b)(a + b) – b(2a + b)
= [a2 + 2ab + b2] – [2ab + b2]
= a2 + 2ab + b2 – 2ab – b2
= a2 combine like terms
foil method and
distributive property
take out brackets
Mr. Sims
Find the value of the determinant.
6.
3
-1
2
2
3
2
1
-1
3
re-copy 1st two columns
4
3
2
-2
2
1
subtract the ups from the downs
draw diagonals
= [3(3)(-2) + (-1)(4)(2) + 2(-2)(1)] – [2(3)(2) + 1(4)(3) + (-2)(-2)(-1)]
= [-18 – 8 – 4] – [12 + 12 – 4]
= -30 – 20
= -50
Mr. Sims
c
Solve the system of equations
by using determinants.
7.
1
x
3x + 5y = 1
-2x + 3y = 12
5
3
5
3
-2
y
3
1
12
5
-2
3
-2
3
3(12)  (2)(1)
y
19
3  60

9  (10)
36  (2)

19
 57

19
38

19
x = -3
a
a
1
12
x
3
1(3)  12(5)
x
3(3)  (2)(5)
c
2
1
2
b
a
1
b
2
b
y
1
b
2
a
a
a
1
2
1
2
c
1
c
2
b
1
b
2
denominator is same as
in determinant for x
y=2
Mr. Sims
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Mr. Sims