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2 years ago

Is (3,8) a solution to this system of eqautions? y=7x+8 y=x+1 Yes or No?

Mathematics

1 answer:

erastova [34]2 years ago

6 0

Answer:

Step-by-step explanation:

plug the numbers in and see if it is true

x=3, y=8

y=7x+8

8=7(3)+8

8=29

is not true, so it is not a solution. even if it might be a solution for the other equation, it is not true for this equation so it is not a solution for this system

how to find an equation: since y=7x+8 and y=x+1, then

7x+8=y, and y=x+1

7x+8=y=y=x+1

7x+8=x+1

6x+8=1

6x=-7

x=-7/6

y=x+1

y=-1/6

solution: (-1 1/6, -1/6)

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1 year ago

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1 year ago

Three friends met for a book club at a coffee shop, each friend ordered a cup of coffee and two donuts. the total of the order w

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Answer:

$Cost\ of\ donut=\frac{49}{24}\approx \$2.042\\\\cost\ of\ donuts=\frac{49}{4}\approx \$12.25$

Step-by-step explanation:

$Let\ cost\ of\ coffee=y\\\\cost\ of\ one\ donut=x\\\\Each\ friend\ buy\ one\ coffee\ and\ two\ donuts\\\\Amount\ for\ 1\ friend=Cost\ of\ coffee+2\times cost\ of\ donut\\\\Amount\ for\ 1\ friend=y+2x\\\\Amount\ required\ for\ 3\ friend=3\times Amount\ for\ 1\ friend\\\\Amount\ required\ for\ 3\ friend=3\times (y+2x)\\\\Amount\ required\ for\ 3\ friend=3y+6x\\\\Total\ bill=\$ 22\\\\3y+2x=22\\\\Given\ cost\ of\ coffee=\$3.25\\\\y=\$3.25$

$Hence\ solution\ of\ following\ system\ of\ equation\ will\ give\ cost\ of\ donut:\\\\3y+6x=22\\\\y=3.25\\\\\\Substitute\ y=3.25\ in\ first\ equation\\\\3\times 3.25+6x=22\\\\9.75+6x=22\\\\6x=22-9.75\\\\6x=12.25\\\\x=\frac{12.25}{6}\\\\x=\frac{49}{24}\approx \$2.042\\\\Cost\ of\ donut=\frac{49}{24}\approx \$2.042$

See attached diagram.

$Each\ friend\ takes\ 2\ donuts\\\\Total\ donuts=Number\ of\ friends\times 2\\\\Total\ donuts=3\times 2=6\\\\cost\ of\ donuts=number\ of\ donuts\times cost\ of\ 1\ donut\\\\cost\ of\ donuts=6\times \frac{49}{24}\\\\cost\ of\ donuts=\frac{49}{4}\approx \$12.25$

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3 years ago