ALGEBRA ONE Name: _____________________________SYSTEMS OF EQUATIONS RETAKE REVIEW

Fundamentals

1. The solution of a system is a _______________________________.

Line Coordinate Point Plane

2. For a point to be a solution to a system, it must make ____________________ equation(s) true.

One Both Neither

3. Graphically and visually, the solution to a system is the _____________________ of the two lines.

Y-Intercepts X-Intercepts Slope Intersection

4. Parallel lines have ________________ solution(s).

One Two No Infinitely Many

5. Infinitely many solutions means that the two lines are ___________________.

Parallel Intersecting the same

6. There are 3 ways to solve a system: _________________________, _____________________, and

___________________.

ExamplesCircle the error in each problem. Explain why it is incorrect and what should have been done. You do not need to solve all the way.

7. Eliminationx+2 y=18 3 x−5 y=30

−3 y=48 y=−16

3 x+2 (−16 )=18 3 x−32=18

3 x=50

x=503

( 503 ,−16)

8. Substitution3 y=3 x−5 2 x= y+8

y=3 ( y+8 )−5 y=3 y+24−5 y=3 y+19

−2 y=19

y=−192

2 x=−192

+8

2 x=−32

x=−34

(−34 ,−192 ) 9. Graphing

y=12x−6

2 y−3 x=6

(−2 ,−6 )

PracticeSolve each system using the method indicated. If no method is indicated, you may choose any method – empty coordinate planes are provided at the end. Check your answers by plugging your solution point back in. When possible, verify your answers using the intersection feature of the graphing calculator (Graph functions, 2ND, Trace [Calc], Intersect, Enter 3 times)

10. Substitutionx=3 y+1 2 x−3 y=6

Check:

11. Elimination5 x+ y=10 x+ y=12

Check:

12. Graphingy=2x−8

y=23x

Check:

13. y=34x+2

y=3 x−7

Check:

14. 3 x+4 y=24

y=−34x−8

Check:

15. x−3 y=−62 x+ y=−12

Check:

Word ProblemsWrite and solve a system for each situation.

16. Jack and Jill went up the hill to fetch some pails of water. Jack’s pail holds twice what Jill’s pail holds. Together, they can carry 9 gallons of water. How much water do Jack and Jill’s pails each hold?

17. Benny is going to the bakery to pick up 37 desserts, cookies and cupcakes, which he ordered for $63. How many cupcakes and cookies did Benny purchase if cookies cost $1.50 and cupcakes cost $2?

18. On Tuesday Johnny and Susie bought a hot chocolate and two apple turnovers for $4.75. The following week, they bought 2 hot chocolates and an apple turnover for $5. How much does an apple turnover and hot chocolate each cost?

SolutionsDetermine if the given point is a solution to the system.

19. (2 ,4 )y=2x 2 x=3 y−5

20. (13 ,−10 )2 x+ y=16 3 y=9−3 x

Extra Coordinate Planes