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(1, 7)
(-2, -1)
No solution
(1, 2)
-x
-x
y = -x + 4
x+y=3
-x
-x
y = -x + 3
(2, 2)
(1, 2)
y > 3x
y < -x
y – 2x > 3
+ 2x + 2x
y > 2x + 3
2y + x > -5
-x -x
2y > -x – 5
2
2 2
y > -1/2x – 5/2
or
y > -0.5x – 2.5
Name
Class
Date
Reteaching (continued)
6-2
Solving Systems Using Substitution
Problem
Solve and check the following system:
x
2 2 3y 5 10
3x 1 4y 5 26
x
2 2 3y 5 10
x
2 5 10 1 3y
Solve
First, isolate x in the first equation.
Add 3y to both sides and simplify.
x 5 20 1 6y
Multiply by 2 on both sides.
3x 1 4y 5 26
Substitute 20 1 6y for x in second equation.
3(20 1 6y) 1 4y 5 26
Simplify.
60 1 22y 5 26
Subtract 60 from both sides.
22y 5 266, y 5 23
Divide by 22 to solve for y.
x
2 2 3(23) 5 10
x
2 1 9 5 10
Substitute 23 in the first equation.
Simplify.
x52
Solve for x.
The solution is (2, 23)..
Check
3(2) 1 4(23) 0 26
26 5 26 3
Now you check the first equation.
Exercises
Solve each system using substitution. Check your answer.
5. 22x 1 y 5 8 (22, 4)
6. 3x 2 4y 5 8 (4, 1)
7. 3x 1 2y 5 25
8. 6x 2 5y 5 3
3x 1 y 5 22
2x 1 3y 5 26
2x 1 y 5 9
(1725, 21335)
x 2 9y 5 25
(22, 23)
Prentice Hall Algebra 1 • Teaching Resources
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