Graphing Graphing SystemsSystems
1
3
2
4
5
1
3
2
4
5
1
3
2
4
5
1
3
2
4
5
11
33
22
44
55
Substitution Substitution MethodMethod
Elimination Elimination MethodMethod ApplicationsApplications Misc.Misc.
Question:
Solve the system graphed.
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Graphing for 1
Answer:
(2, 3)
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Graphing for 1
Question:
If the equations of a system are graphed to be parallel lines, what is the solution?
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Graphing for 2
Answer:
no solution
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Graphing for 2
Question:
If a system has infinitely many solutions, what occurs when solving using the graphing method?
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Graphing for 3
Answer:
You get coinciding lines.
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Graphing for 3
Question:
Solve by graphing.
x + y = -1
y = 4x + 4
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Graphing for 4
Answer:
(-1, 0)
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Graphing for 4
Question:
State the system shown.
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Graphing for 5
Answer:
y = 2x - 3
y = -x + 4
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Graphing for 5
Question:
When is it best to use the substitution method when solving systems?
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Substitution for 1
Answer:
When one of the equations is solved for one variable.
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Substitution for 1
Question:
Solve by substitution.
y = 2x – 3
y = 6 – x
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Substitution for 2
Answer:
(3, 3)
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Substitution for 2
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Substitution for 3
Question:
Solve by substitution.
x = 3y + 5
2x + y = 3
Answer:
(2, -1)
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Substitution for 3
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Substitution for 4
Question:
Solve by substitution.
5x – y = 2
y = 5x + 3
Answer:
no solution
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Substitution for 4
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Substitution for 5
Question:
Solve by substitution.
3x – y = 11
y = 4x – 15
Answer:
(4, 1)
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Substitution for 5
Question:
When is it best to use the elimination method for solving systems?
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Elimination for 1
Answer:
When both equations are in standard form.
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Elimination for 1
Question:
Solve by elimination.
x – 2y = 5
3y + 2y = –1
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Elimination for 2
Answer:
(1, -2)
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Elimination for 2
Question:
Solve by elimination.
3x – 5y = 0
–x + 2y = 2
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Elimination for 3
Answer:
(10, 6)
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Elimination for 3
Question:
Solve by elimination.
2x – 3y = –1
–6x + 9y = 3
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Elimination for 4
Answer:
infinitely many solutions
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Elimination for 4
Question:
Solve by elimination.
4x + 3y = –18
5x – 2y = –11
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Elimination for 5
Answer:
(-3, -2)
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Elimination for 5
Question:
Solve by graphing.
y > x – 3
y < 5 – x
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Inequalities for 1
Answer:
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Inequalities for 1
Question:
Solve by graphing.
y ≥ x
x < 3
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Inequalities for 2
Answer:
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Inequalities for 2
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Inequalities for 3
Question:
Solve by graphing.
2x – 3y > 12
y > (-1/2)x – 3
Answer:
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Inequalities for 3
Question:
Is (3, -5) a solution to:
y > 2 – 7x
2x – 3y < 9
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Inequalities for 4
Answer:
No; it fails the second inequality.
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Inequalities for 4
Question:
State the system shown.
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Inequalities for 5
Answer:
y ≥ –2
y < x – 1
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Inequalities for 5
Question:
Solve for x.
3x – 7y = 12
2x + 2y = 5
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Miscellaneous for 1
Answer:
x = 59/20
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Miscellaneous for 1
Question:
Solve by graphing.
y = 3x + 2
6x – 2y = –4
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Miscellaneous for 2
Answer:
infinitely many solutions
(the lines are coinciding)
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Miscellaneous for 2
Question:
Two numbers add to 9. One is 5 more than the other. What are the numbers?
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Miscellaneous for 3
Answer:
7 and 2
x + y = 9
x = y + 5
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Miscellaneous for 3
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Miscellaneous for 4
Question:
You buy 25 CD’s with some on sale at $10 and others at $15. If you spent $315, how many were on sale?
Answer:
12 were on sale
x + y = 25
10x + 15y = 315
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Miscellaneous for 4
Question:Graph
x > 1
y > 1
y ≤ 4 – 2x
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Miscellaneous for 5
Answer:
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Miscellaneous for 5