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alekssr [168]
3 years ago
10

5x + 4y = 11 2x + 6y = -7

Mathematics
1 answer:
olga55 [171]3 years ago
8 0

\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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Answer:

Person A made 108 cupcakes and person B made 60 cupcakes.

Step-by-step explanation:

Person A makes 1 cupcake in 5 minutes.

Say in x minutes A makes : \frac{x}{5} cupcakes

Person B makes 1 cupcake in 9 minutes.

Say in x minutes B makes : \frac{x}{9} cupcakes

Total cupcakes prepared by A and B in x minutes = 168

\frac{x}{5}+\frac{x}{9}=168

\frac{14x}{45}=168

x=\frac{168\times 45}{14}=540

So, cupcakes made by A = \frac{540}{5}=108

Cupcakes made by B = \frac{540}{9}=60

Person A made 108 cupcakes and person B made 60 cupcakes.

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For line 3x-y-7 <0, let's disregard < first and change it to =, such that 3x-y-7=0. Rearranging, y=3x-7. If you plot this equation, that would be the blue line in the equation. To know which of side of the line is the solution, you substitute a random point into the equality. For example, let's use point (5,20).

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