Name ________________________________________ Date __________________ Class__________________
LESSON
6-3
Practice B
Solving Systems by Elimination
Follow the steps to solve each system by elimination.
⎧3x + y = 17
2. ⎨
⎩4x + 2y = 20
⎧2x − 3y = 14
1. ⎨
⎩2x + y = −10
Multiply the first equation by −2. Then,
add the equations:
Subtract the second equation:
2x – 3y = 14
___
− (2x + y = −10)
x − __ y = _____
+ 4x + 2y = 20
_________________________________________
________________________________________
Solve the resulting equation:
Solve the resulting equation:
y = _____________
x = _____________
Use your answer to find the value of x:
Use your answer to find the value of y:
x = _____________
y = _____________
Solution: ( _____, _____ )
Solution: ( _____, _____ )
Solve each system by elimination. Check your answer.
⎧ x + 3y = −7
3. ⎨
⎩−x + 2y = −8
________________________
⎧4x − y = −5
6. ⎨
⎩−2x + 3y = 10
________________________
⎧3x + y = −26
4. ⎨
⎩2x − y = −19
_________________________
⎧
7. ⎨ y − 3x = 11
⎩2y − x = 2
_________________________
⎧ x + 3y = −14
5. ⎨
⎩2x − 4y = 32
________________________
⎧−10x + y = 0
8. ⎨
⎩5x + 3y = −7
________________________
Solve.
9. Brianna’s family spent $134 on 2 adult tickets and 3 youth tickets
at an amusement park. Max’s family spent $146 on 3 adult tickets
and 2 youth tickets. What is the price of a youth ticket?
___________________________
10. Carl bought 19 apples of 2 different varieties to make a pie.
The total cost of the apples was $5.10. Granny Smith apples
cost $0.25 each and Gala apples cost $0.30 each. How many
of each type of apple did Carl buy?
___________________________
___________________________
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6-20
Holt McDougal Algebra 1
Name ________________________________________ Date __________________ Class__________________
LESSON
6-3
Practice C
Solving Systems by Elimination
Solve each system by elimination.
⎧x + y = 2
1. ⎨
⎩2x − y = 7
________________________
⎧−3x − 4y = −2
4. ⎨
⎩6x + 4y = 3
________________________
⎧ x + 6y = 1
7. ⎨
⎩2x − 3y = 32
________________________
⎧5x − 2y = −48
10. ⎨
⎩2x + 3y = −23
________________________
⎧3x − 2y = −2
2. ⎨
⎩3x + y = 10
⎧ x + y = −7
3. ⎨
⎩x − y = 5
_________________________
________________________
⎧2x − 2y = 14
5. ⎨
⎩ x + 4y = −13
⎧
6. ⎨ y − x = 17
⎩2y + 3x = −11
_________________________
________________________
⎧ 1
⎪⎪− x + y = 4
8. ⎨ 2
⎪ 1 x − y = −3
⎪⎩ 3
⎧3x + y = −15
9. ⎨
⎩2x − 3y = 23
_________________________
________________________
⎧4x − 3y = −9
11. ⎨
⎩5x − y = 8
⎧3x − 3y = −1
12. ⎨
⎩12x − 2y = 16
_________________________
________________________
13. At a bakery, Riley bought 3 bagels and 2 muffins for $7.25.
Karen bought 5 bagels and 4 muffins for $13.25. What is
____________________________________
the cost of each item?
14. A chemist has a beaker of a 3% acid solution and a beaker of
a 7% acid solution. He needs to make 75 mL of a 4% acid solution.
a. Complete the table.
Amount of Solution (mL)
Amount of Acid (mL)
3% solution
+
7% solution
=
4% solution
x
+
y
=
________
+
_____ y
=
0.04(75)
_____
x
b. Use the information in the table to write a system of
linear equations.
_____________________________________
c. Solve the system of equations to find how much he
will use from each beaker.
_________________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
6-21
Holt McDougal Algebra 1