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1 answer:
Answer:
The expressions that give the value of y are A - 3B and (1/3)A - B
The solution is (27/13, -60/13)
Step-by-step explanation:
We can see both equation A and equation B.
Equation A: 2x + (1/4)y = 3
Equation B: (2/3)x - y = 6
To find the value of y, we have to solve both equations A and equation B simultaneously. This is done by multiplying equation B by 3 and subtracting from equation A (A - 3B) to get:
(13/4)y = -15
y = -60/13
you can also get y by dividing equation A by 3 and subtracting equation B (1/3A - B)
Put y = -60/13 in equation A to get x:
2x + (1/4)(-60/13) = 3
2x = 3 + 15/13
2x = 54/13
x = 27/13
The solution is (27/13, -60/13)
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Answer:
x = π/3, x = 5π/3, x = 4π/3
Step-by-step explanation:
Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3 = 0.
Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.
Similarly:
The general solutions for sin(x) = - √3/2 are x = 4π/3 + 2πn and x = 5π/3 + 2πn. Therefore x = 4π/3 and x = 5π/3 in this case.
So we have x = π/3, x = 5π/3, and x = 4π/3 as our solutions.