Graphing systems
Solve by graphing:
y = x + 1
y = -x + 5
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(2, 3)
Solve using substitution:
y = x + 2
x + y = 6
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(2, 4)
Solve using elimination:
x + y = 10
x - y = 2
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(6, 4)
Rewrite in exponential form:
√x
x¹ᐟ²
Two numbers add to 10. One is 2 more than the other.
Find the numbers.
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4 and 6
Solve by graphing:
y = 2x - 4
y = -x + 5
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(3, 2)
Solve using substitution:
y = 2x
3x + y = 12
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(3, 6)
Solve using elimination:
2x + y = 7
2x - y = 1
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(2, 3)
Rewrite in exponential form:
³√x²
x²ᐟ³
The sum of two numbers is 18. The difference between the numbers is 6.
Find the numbers.
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12 and 6
Solve by graphing:
y = x - 2
y = x + 3
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No solution (parallel lines)
Solve using substitution:
y = x - 1
2x + y = 11
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(4, 3)
Solve using elimination:
3x + 2y = 12
3x - 2y = 4
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(8/3, 2)
Rewrite in radical form:
x³ᐟ⁵
⁵√(x³)
A movie theater sells adult tickets for $10 and student tickets for $5.
Total tickets sold: 20
Total revenue: $150
Find how many of each were sold.
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10 adults, 10 students
Solve by graphing:
y = -2x + 6
y = -2x + 6
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Infinite solutions (same line)
Solve using substitution:
y = 3x + 2
2x - y = 4
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(-6, -16)
Solve using elimination:
2x + 3y = 13
4x + 3y = 19
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(3, 7/3)
Rewrite in exponential form:
⁴√(x³)
x³ᐟ⁴
The perimeter of a rectangle is 50.
Length is 5 more than width.
Find the dimensions.
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width = 10, length = 15
Solve by graphing:
y = ½x + 1
y = -3/2 x + 5
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(2, 2)
Solve using substitution:
y = 2x - 5
3x + 2y = 4
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(2, -1)
Solve using elimination:
3x + 2y = 6
6x + 4y = 12
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Infinite solutions
Rewrite in radical form:
x⁵ᐟ²
²√(x⁵) OR √(x⁵)
A gym charges $20 membership fee plus $5 per visit. Another gym charges $10 membership fee plus $7 per visit.
After how many visits will the cost be the same?
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5 visits