What is the first step in solving the system shown using the shown using the elimination method? (3x - 12y = 5 | 3y - x = 9 A. M
2 answers:
Answer: OPTION C.
Step-by-step explanation:
Given a System of equations, you can use the Elimination Method to solve it by transforming the system in order to cancel out one of the variables. But first, the terms of both equations must be written in the same order.
To cancel out one of the variables, the coefficients must be opposites, which means that one must be positive and the other one must be negative.
Given the following System of equations:
You can notice that the order of the terms is not the same, so, if you want to use the Elimination Method to solve the system of equations, the first step you must apply is to rewrite the equations so like variable terms are in the same order.
Then:
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Answer:
(-2, -3)
Step-by-step explanation:
A careful graph shows the point (-2, -3) is at the intersection of the circles whose radii are the given distances from the receiving stations.
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The simultaneous equations for the circles can be solved algebraically.
The epicenter is 10 units from X, so lies on the circle ...
(x -4)^2 +(y -5)^2 = 10^2
x^2 -8x +16 +y^2 -10y +25 = 100
x^2 +y^2 -8x -10y = 59
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The epicenter is 5 units from Y, so lies on the circle ...
(x +6)^2 +(y +6)^2 = 5^2
x^2 +12x +36 +y^2 +12y +36 = 25
x^2 +y^2 +12x +12y = -47
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The epicenter is 13 units from Z, so lies on the circle ...
(x +14)^2 +(y -2)^2 = 13^2
x^2 +28x +196 +y^2 -4y +4 = 169
x^2 +y^2 +28x -4y = -31
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Subtracting the second equation from each of the other two, we get ...
(x^2 +y^2 -8x -10y) -(x^2 +y^2 +12x +12y) = (59) -(-47)
-20x -22y = 106 . . . . eq1 -eq2
(x^2 +y^2 +28x -4y) -(x^2 +y^2 +12x +12y) = (-31) -(-47)
16x -16y = 16 . . . . . . . .eq3 -eq2
These simultaneous linear equations can be solved a variety of ways. We might use substitution:
x = y+1 . . . . . from eq3 -eq2 divided by 16
10(y +1) +11y = -53 . . . . . from eq1 -eq2 divided by -2
21y = -63 . . . . . . . . . . . . simplify, subtract 10
y = -3
x = y+1 = -2
The epicenter is located at (x, y) = (-2, -3).
