Name ________________________________________ Date __________________ Class__________________
LESSON
x-x
5-3
Practice B
Solving Systems by Elimination
Follow the steps to solve each system by elimination.
⎧2x − 3y = 14
1. ⎨
⎩2x + y = −10
⎧3x + y = 17
2. ⎨
⎩4x + 2y = 20
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?
___________________________
___________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-20
Holt McDougal Algebra 1
5-3 SOLVING SYSTEMS BY ELIMINATION
Review for Mastery
Practice A
1. 0y; 3x; 3; 3; 2; 2; 2; 2; 2; 12; 4; 2; 4
2. 2y; −7; 0y; −3; −3; −1; −1; 3; 3; 3; 9; 9; 9;
−2; 2; 2; −1; 3; −1
3. 2; 4; −16; 5; 10; 5; 10; 5; 5; 2; 2; 2; 2; 2;
−10; −2; −2; 5; 2; 5
4. (3, 4)
5. (6, −2)
6. (−8, −1)
7. 3 and −4
⎛ 1 ⎞
6. ⎜ − , 3 ⎟
⎝ 2 ⎠
7. (−4, −1)
⎛ 1
⎞
8. ⎜ − , −2 ⎟
⎝ 5
⎠
9. $22
4. (−4, −14)
5. (7, 10)
6. (7, −18)
⎧5 x + 4 y + z = 865
1. ⎨
⎩9 x + 6 y + 6z = 1410
2. 5x − 2y = 20
3. −21x − 18y = −3780
4. x = 60
2. −6; 2; −34; −2x = −14; 7; −4; 7; −4
5. (4, −6)
3. (−6, 18)
Challenge
1. −4y = 24; −6; −2; −2; −6
4. (−9, 1)
2. (4, −1)
7. (5, −2)
Practice B
3. (2, −3)
1. (3, −14)
⎧2y + z = 285
5. ⎨
⎩ 4 y + z = 565
6. y = 140, z = 5
7. sleeping bags: $60; tents: $140;
bug repellant: $5
Problem Solving
1. chicken leg 8 oz.,
10. 7 Gala apples; 12 Granny Smith apples
chicken wing 3 oz.
Practice C
2. bath towel $10,
1. (3, −1)
2. (2, 4)
3. (−1, −6)
⎛ 1 1⎞
4. ⎜ , ⎟
⎝3 4⎠
3. adult ticket $8,
5. (3, −4)
6. (−9, 8)
4. office visit $25,
7. (13, −2)
8. (−6, 1)
allergy shot $8
9. (−2, −9)
10. (−10, −1)
11. (3, 7)
⎛5 ⎞
12. ⎜ , 2 ⎟
⎝3 ⎠
hand towel $5
child ticket $5
5. A
6. G
Reading Strategies
1. Multiply the first equation by 3 and the
second equation by 5 to get common
coefficients of −15.
13. bagel: $1.25; muffin: $1.75
14. 75; 0.03; 0.07
⎧ x + y = 75
⎨
⎩0.03 x + 0.07 y = 3
⎧4(9 x − 10 y = 7) ⎧36 x − 40 y = 28
⇒⎨
2. ⎨
⎩5(5 x + 8 y = 31)
⎩25 x + 40 y = 155
56.25 mL of the 3% solution; 18.75 mL
of the 7% solution
3. (1, −3)
4. (10, −10)
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A62
Holt McDougal Algebra 1