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# Need help, again!

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Find the ordered pair  that satisfies the system of equations

\begin{align*} x+3y &= -4,\\ 3x -7y &= 36. \end{align*}

Nov 10, 2018

#1
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subtract 3x the first equation from the second equation

$$(3x-7y)-3(x+3y) = 36 - 3(-4)\\ -16y=48\\ y=-3\\ \text{use this value of y to obtain x}\\ x + 3(-3) = -4 \\ x - 9 = -4\\ x = 5\\ (x,y) = (5,-3)$$

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Nov 10, 2018
#2
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Substitution: x+3y=-4, so x=-4-3y and 3(-4-3y)-7y=36, -12-9y-7y=36, -9y-7y=48, -16y=48, y=-3. and x=x+3(-3)=-4, x-9=-4, x=5. Thus, the ordered pair is (5, -3).

Elimination: We can also show this by elimination: multiply the first equation by 3, which yields, 3x+9y=-12 and 3x-7y=36. Subtract, 16y=-48, y=-3. Plugging the value of y back in to find the value of x, we get x+3(-3)=-4, x-9=-4, x=5. Thus, the ordered pair is (5, -3).

Nov 11, 2018