Answer:
x = 5
Step-by-step explanation:
4x + 2y + z = 24
2x - 3y - z = 2
5x + y + 2z = 21
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Eliminate z
Add the 1st and 2nd eqn
4x + 2y + z = 24
2x - 3y - z = 2
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6x - 1y = 26 eqn A
Multiply the 2nd eqn by 2, then add the 3rd.
4x - 6y -2z = 4
5x + y + 2z = 21
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9x - 5y = 25 eqn B
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Now you have 2 eqns in 2 unknowns, not 3.
Multiply eqn A by 5 and subtract eqn B.
30x - 5y = 130 eqn A times 5
9x - 5y = 25 eqn B
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21x = 105
x = 5
Recall that variation of parameters is used to solve second-order ODEs of the form
<em>y''(t)</em> + <em>p(t)</em> <em>y'(t)</em> + <em>q(t)</em> <em>y(t)</em> = <em>f(t)</em>
so the first thing you need to do is divide both sides of your equation by <em>t</em> :
<em>y''</em> + (2<em>t</em> - 1)/<em>t</em> <em>y'</em> - 2/<em>t</em> <em>y</em> = 7<em>t</em>
<em />
You're looking for a solution of the form
where
and <em>W</em> denotes the Wronskian determinant.
Compute the Wronskian:
Then
The general solution to the ODE is
which simplifies somewhat to
The rule for negative exponents is that if the exponent is negative to begin with, in order to make it negative, you put it into the denominator of a fraction, and raise it to whatever the power is. To go from positive exponents (those that are already in the denominator), move it up to the numerator and make the exponent negative. So your solution would be 5x^-2
What does it say I can’t see
