Solve 5x+4y=-30 3x-9y=-18 Solve using the elimination method
1 answer:
Answer:
(x, y) = (-6, 0)
Step-by-step explanation:
The y-coefficients have opposite signs, so we can eliminate y-terms by multiplying both equations by a positive number and adding the results.
9 times the first equation plus 4 times the second gives ...
9(5x +4y) +4(3x -9y) = 9(-30) +4(-18)
45x +36y +12x -36y = -270 -72 . . . . eliminate parentheses
57x = -342 . . . . . collect terms
x = -6 . . . . . . . divide by the coefficient of x
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Substituting into the first equation gives ...
5(-6) +4y = -30
4y = 0 . . . . . . . . . add 30
y = 0
The solution is (x, y) = (-6, 0).
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Answer:
2
Step-by-step explanation:
The given angle is opposite the <em>shortest</em> of the given sides, and sin(A) < 5/6, so there are two possible solutions.
The law of sines tells you that angle C will satisfy ...
sin(C)/ab = sin(A)/bc
sin(C) = ab/bc·sin(A) = 6/5·1/2 = 3/5
The given angle is 30°, so the sum of remaining angles must be less than 150°. There are two possible angles less than 150° that have a sine of 3/5:
C₁ = arcsin(3/5) = 36.87°
C₂ = 180° -arcsin(3/5) = 143.13°
You can construct two triangles with the given measurements.
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See the attachments for drawings of them.
