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Mr. Sims
Algebra 1
Section 7.2 C
Substitution
Use substitution to solve the linear system.
1. y = x – 4
2. -3x = 9
x = -3
3x – y = - 8
3x – (x – 4) = - 8 substitute for y
3x – x + 4 = - 8 take out parentheses
2x + 4 = - 8 combine like terms
-4
-4
2x + y = -13
2(-3) + y = -13
-6 + y = -13
+6
substitute for x
+6
y = -7
2x = -12
x = -6
y=x–4
y = -6 – 4
y = -10
substitute for x
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3. -3x + y = -18
x – y = 14
+y
get one equation to read
x = or y =
+y
x = y + 14
-3(y + 14) + y = -18 substitute for x
-3y – 42 + y = -18 distributive property
-2y – 42 = - 18 combine like terms
+42
+42
-2y = 24
y = -12
x = y + 14
x = -12 + 14
x=2
4. -3x + y = -3
+3x
+3x
y = 3x – 3
2x – 5y = -11
2x – 5(3x – 3) = -11 substitute for y
2x – 15x + 15 = -11 distributive prop.
-13x + 15 = -11 combine like terms
-15
-15
-13x = -26
x=2
y = 3x - 3
y = 3(2) – 3
y=6–3
y=3
substitute for x
substitute for y
Mr. Sims
5. 2x – 3y = -14
3x – y = -7
-3x
get one equation to
read x = or y =
-3x
-y = -3x – 7
y = 3x + 7 divide by -1
2x – 3(3x + 7) = -14 substitute for y
2x – 9x – 21 = -14 distributive property
-7x – 21 = -14 combine like terms
+21
+21
-7x = 7
x = -1
y = 3x + 7
y = 3(-1) + 7
y = -3 + 7
y=4
6. 1 x  y  3
2
-½x
- ½x
1
y   x3
2
2x + 3y = 10
 1

2x  3  x  3   10 substitute for y
 2

3
2x  x  9  10 distributive property
2
1
x  9  10 combine like terms
2
1
-9 -9
y   x3
2
1
x 1
2
1
y   (2)  3
2
x=2
y = -1 + 3
y=2
Mr. Sims
1
7.
3
x
2
1
2
x

y2
8. 10
5
y  12
3
1
x + 9y = -6
-9y
2
-½x
-9y
x = - 9y – 6
1
( 9y  6) 
3
2
x  y  10
y  12 substitute for x
3
-½x
y
x = 48
21
x = 20
1
x  10
2

x   x  10   2
10
52

1
2
 3y  2  y  12 distributive property
3
1
1
x x42
7
10
5
 y  2  12 combine like terms
3
1
- x42
+2 +2
x = -9y - 6
10
-4 -4
7
 y  14
1
x
=
-9(-6)
–
6
x  2
3
10
= 54 – 6
y=-6
1
 y   x  10
2
y
1
x  10
2
1
y  (20)  10
2
y = 10 – 10
y=0
Mr. Sims
Use the substitution method to solve the linear system.
1.) -x + 3y = 4
x + 6y = 14
2.) 3x + 2y = 8
x + 4y = - 4
3.) x – 5y = - 3
4x – 3y = 5
4.) 2x + 5y = 4
x + 5y = 7
5.) 1 x + y = 2
6.)
2
2x 3y = 9
Algebra 1
Section 7.2 C
Assignment
1
5
x  y 1
3
6
1
 x  y 1
2
Mr. Sims
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