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Mr. Sims
Solve with the substitution method.
1.
Algebra 1
Sect. 7.4 C
Review System
of Equations
3x – y = 9
2x + y = 6
-2x
get one equation to
read x = or y =
y = -2x + 6
-2x
3x – (-2x + 6) = 9
3x + 2x – 6 = 9
5x – 6 = 9
take out parentheses
combine like terms
+6 +6
5x = 15
x=3
y = -2x + 6
y = -2(3) + 6
y = -6 + 6
y=0
substitute into most efficient
equation to solve for y
Mr. Sims
Solve with the addition method.
2.
-2x + 3y = 14
2 x – 4y = -12
multiply to cancel
variable when added
-2x + 3y = 14
2x – 8y = -24
-5y = -10
y=2
x – 4y = -12
x – 4(2) = -12
x – 8 = -12
+8
substitute into any
equation with x and y
+8
x=-4
Mr. Sims
Solve with the substitution method.
3.
2x – y = 3
-2x
y = 2x – 3
-y = -2x + 3
divide by -1
-2x
3x – y = 4
get one equation to
read x = or y =
3x – (2x – 3) = 4
3x – 2x + 3 = 4
x+3=4
watch signs {put in parentheses}
take out parentheses
combine like terms
-3 -3
x=1
y = 2x - 3 substitute into most efficient
equation to solve for y
y = 2(1) – 3
y=2–3
y = -1
Mr. Sims
Solve with the addition method.
4.
3 -x + 8y = 16
3x + 4y = 36
multiply to cancel
variable when added
-3x + 24y = 48
3x + 4y = 36
28y = 84
y=3
3x + 4y = 36
3x + 4(3) = 36
3x + 12 = 36
substitute into any
equation with x and y
-12 -12
3x = 24
x=8
Mr. Sims
Solve with the substitution method.
5.
x – 5y = -3
+5y
x = 5y - 3
+5y
4x – 3y = 5
get one equation to
read x = or y =
4(5y – 3) – 3y = 5
20y – 12 – 3y = 5
17y – 12 = 5
distributive property
combine like terms
+12 +12
17y = 17
y=1
x = 5y – 3
substitute into most efficient
equation to solve for x
x = 5(1) – 3
x=5–3
x=2
Mr. Sims
Solve with the addition method.
6.
5x + 2y = 5
-2 3x + y = 2
5x + 2y = 5
-6x – 2y = - 4
-x = 1
x = -1
5x + 2y = 5
5(-1) + 2y = 5
-5 + 2y = 5
+5
substitute into any
equation with x and y
+5
2y = 10
y=5
Mr. Sims
Solve with the substitution method.
7.
½x + y = 2
-½x
y = -½x + 2
-½x
2x + 3y = 9
get one equation to
read x = or y =
2x + 3(-½x + 2) = 9
3
2x  x  6  9
2
distributive property
½x + 6 = 9
combine like terms
-6 -6
½x = 3
x=6
y = -½x + 2
y = -½(6) + 2
y = -3 + 2
y = -1
substitute into most efficient
equation to solve for y
Mr. Sims
Solve with the addition method.
8.
5 -7x + 8y = 32
7 5x + 6y = 24
multiply to cancel
variable when added
-35x + 40y = 160
35x + 42y = 168
82y = 328
y=4
5x + 6y = 24
5x + 6(4) = 24
5x + 24 = 24
substitute into any
equation with x and y
-24 -24
5x = 0
x=0
Mr. Sims
Algebra 1
Sect. 7.4 C
Assignment
Solve with the substitution method.
1.) 3x – 4y = 6
-x + y = -1
2.) 4x – 3y = -2
4x + y = 4
3.) -2x + y = 4
4x – 3y = -7
4.) 3x + y = 11
x + 2y = -3
Solve with the addition method.
5.) 3x + 5y = -16
-2x + 6y = -36
6.) 2x – 15y = -20
-4x + 5y = 5
Mr. Sims
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Mr. Sims