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```Mr. Sims
Algebra 1
Solve with the substitution method.
1.
Sect. 7.4 B
Review of System of
Equations
2x + y = 5
x–y=1
x=y+1
+y +y
get one equation to
read x = or y =
2(y + 1) + y = 5
2y + 2 + y = 5
3y + 2 = 5
distributive property
combine like terms
-2 -2
3y = 3
y=1
x=y+1
x=1+1
x=2
substitute into most efficient
equation to solve for x
Mr. Sims
2. 3 2x – y = 3
4x + 3y = 21
multiply to cancel out
6x – 3y = 9
4x + 3y = 21
10x = 30
x=3
4x + 3y = 21
substitute into any
equation with x and y
4(3) + 3y = 21
12 + 3y = 21
-12
-12
3y = 9
y=3
Mr. Sims
Solve with the substitution method.
3.
x – 2y = 4
x = 2y + 4
+2y +2y
6x + 2y = 10
get one equation to
read x = or y =
6(2y + 4) + 2y = 10
12y + 24 + 2y = 10
14y + 24 = 10
-24
distributive property
combine like terms
-24
14y = -14
y = -1
x = 2y + 4
x = 2(-1) + 4
x = -2 + 4
x=2
substitute into most efficient
equation to solve for x
Mr. Sims
4. 2 3x + 6y = 8
-6x + 3y = 2
multiply to cancel out
6x + 12y = 16
-6x + 3y = 2
15y = 18
4
3x 
5
4
x
15
18
y
15
6
y
5
3x + 6y = 8
6
3x  6   8
5
36
3x   8
5
-36/5
substitute into any
equation with x and y
-36/5
Mr. Sims
Solve with the substitution method.
5.
x+y=0
-y
x = -y
-y
3x + 2y = 1
get one equation to
read x = or y =
3(-y) + 2y = 1
-3y + 2y = 1
-y = 1
y = -1
x = -y
x = -(-1)
x=1
substitute into most efficient
equation to solve for x
Mr. Sims
6. -3 2x – 3y = -7
2 3x + y = -5
-6x + 9y = 21
6x + 2y = -10
multiply to cancel out
11y = 11
y=1
3x + y = -5
3x + 1 = -5
substitute into any
equation with x and y
-1 -1
3x = -6
x = -2
Mr. Sims
Algebra 1
Sect. 7.4 B
Assignment
Use the substitution method to solve the system.
1.) x + y = 2
-3x + 4y = 15
2.) x – y = -8
7x + 5y = 16
3.) x + 5y = 17
-4x + 3y = 24
Use the addition method to solve the system.
4.) 6x + y = -39
3x + 2y = -15
5.) 2x + 5y = 11
4x + 3y = 1
6.) 3x – 3y = -6
-5x + 6y = 12
Mr. Sims
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