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Answer:
(x, y) = (10, - 1)
Step-by-step explanation:
given the 2 equations
3y = - x + 2 → (1)
y = - x + 9 → (2)
substitute y = - x + 9 into (1)
3(- x + 9) = - x + 2
- 3x + 27 = - x + 2
add x to both sides
- x + 27 = 2 ( subtract 27 from both sides )
- x = - 25
multiply both sides by 2 and divide by - 5
x = 10
solution (10, - 1)
Answer:
- ribbon: $0.45
- markers: $0.08
Step-by-step explanation:
Each purchase will be the sum of products of item price and number of items. The two purchases give rise to two equations.
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<h3>equations</h3>The variables are defined in the problem statement. The two purchases are ...
11r +16m = 6.23
13r +7m = 6.41
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<h3>solution</h3>A calculator offers a simple way to find the solutions to these equations. The attachments show the solution to be ...
- r = 0.48
- m = 0.08
The cost of ribbon is $0.45; the cost of a marker is $0.08.
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The "cross-multiplication" method of solving these equations seems particularly useful when the coefficients are mutually prime. It starts with a rewrite to general form:
- 11r +16m -6.23 = 0
- 13r +7m -6.41 = 0
Then we define three "cross products":
Δ1 = (11)(7) -(13)(16) = -131
Δ2 = (16)(-6.41) -(7)(-623) = -58.95
Δ3 = (-6.23)(13) -(-6.41)(11) = -10.48
The solutions are ...
r = Δ2/Δ1 = -58.95/-131 = 0.45
m = Δ3/Δ1 = -10.48/-131 = 0.08
The cost of ribbon is $0.45; the cost of a marker is $0.08.
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For more about the cross-multiplication method you can read ...
