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photoshop1234 [79]
3 years ago
14

How would I solve y=5x-2 & -14x+y=16 in a substitution equation

Mathematics
1 answer:
Aleks04 [339]3 years ago
7 0
You would substitute the given value of “y” into the equation of -14x+y=16
-14x+5x-2=16

Then you would solve for “x”
x=2

You would then substitute the value of “x” into the equation to solve for “y”
y=5(2)-2

Which would then give you a value for “y”
y=12
So the answer is (2,12)

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\left\{\begin{array}{ccc}5x+4y=11&|\cdot2\\2x+6y=-7&|\cdot(-5)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}10x+8y=22\\-10x-30y=35\end{array}\right}\ \ \ \ |add\ both\ sides\ of\ the\ equations\\.\ \ \ \ \ \ \ \ \ \ \ -22y=57\ \ \ \ |:(-22)\\.\ \ \ \ \ \ \ \ \ \ \ y=-\dfrac{57}{22}\\\\substitute\ the\ value\ of\ y\ to\ the\ first\ equation\\\\5x+4\left(-\dfrac{57}{22}\right)=11\\\\5x-2\cdot\dfrac{57}{11}=11\ \ \ \ |\cdot11\\\\55x-114=121\ \ \ \ |+114\\\\55x=135\ \ \ \ |:55

x=\dfrac{135}{55}\\\\x=\dfrac{27}{11}\\\\Answer:\ x=\dfrac{27}{11}\ and\ y=-\dfrac{57}{22}\to\left(\dfrac{27}{11},\ -\dfrac{57}{22}\right)

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