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3 years ago

Solve the following system of equations using the substitution method

Mathematics

2 answers:

Alecsey [184]3 years ago

4 0

Answer:

x = -5

y = -3

Step-by-step explanation:

Two equations

Solve using substitutition

y = -3

y - 3x = 12

_____________________

Since the first equation has y alone, we can plug it into the second equation for y.

(-3) - 3x = 12

-3 - 3x = 12

Add 3 to both sides :

-3x = 15

Divide -3 from both sides to get x alone :

x = -5

Now that we have x, plug it into x in the second equation :

y - 3(-5) = 12

y + 15 = 12

Solve for y :

Subtract 15 from both sides :

y = -3

Nikitich [7]3 years ago

3 0

Answer:

x = 5

y = -3

as an ordered pair: (5,-3)

Step-by-step explanation:

if y = -3, then replace y in the first equation with -3.

-3 - 3x = 12

move -3 over to the other side by adding 3 to both sides.

3x = 15

x = 5

y = -3

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Which expression is equivalent to (9x - 3 1/8) - (7x + 1 3/8)?

serg [7]

STEPS TO GET THE CORRECT ANSWER:

First write your question like this:
{ ( [9x] [-31/8] ) - ( [7x] [+13/8] ) }

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3: Then need to subtract -31/8 from +13/8. You get -11/2.
Turn -11/2 into a mixed number you will get -5 1/2.

4: Put 2x and -5 1/2 together and you would get 2x-5 1/2

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ANSWER: C.) 2x-4 1/2

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4 years ago

209,767 rounded to the nearest hundred thousand

GaryK [48]

209,767 rounded to the nearest hundred thousand (Or nearest 100,000) is 200,000.

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3 years ago

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A confectioner has 300 pounds of a chocolate that is 1 part cocoa butter to 7 parts caramel. How much chocolate that is 1 part c

anygoal [31]

Let's call our unknown quantity $n$ . We'll need to add $n$ lbs of chocolate with a 1/15 ratio of cocoa butter to caramel to 300 lbs of chocolate with a 1/7 ratio of cocoa butter to caramel to yield $300+n$ lbs of chocolate with a 1/9 ratio of cocoa butter to caramel. We can set this up as an equation, but it's important to note something first: the ratio of the <em>caramel to the cocoa butter</em> is provided, but this is not the same thing as the <em>fraction of the chocolate the cocoa butter takes up</em>.

The 300 pounds of chocolate have 1 + 7 = 8 parts of cocoa butter and caramel total, which means that cocoa butter takes up 1/8 of those total parts; the $n$ pounds we're adding on has 1 + 15 = 16 total parts, which means the cocoa butter takes up 1/16 of those; and the $300+n$ pounds being produced have 1 + 9 = 10 total parts, so the cocoa butter takes up 1/10 of those parts. With this in mind, we can set up the following equation:

$300\big( \frac{1}{8}\big)+n\big( \frac{1}{16}\big)=(300+n)\big( \frac{1}{10}\big)$

which we can rewrite as

$\frac{300}{8}+ \frac{n}{16}= \frac{300+n}{10}$

From here, it would be helpful to combine the fractions on the left side of the equation. To do this, we'll convert the denominator of $\frac{300}{8}$ to 16, multiplying it by $\frac{2}{2}$ to obtain the fraction $\frac{600}{16}$ . Combining that with $\frac{n}{16}$ , we have:

$\frac{600+n}{16}= \frac{300+n}{10}$

To get rid of the denominator on the left, we'll multiply both sides of the equation by 16, and to eliminate the one on the right, we'll multiply both sides by 10:

$(10)(16)\big( \frac{600+n}{16}\big)=\big( \frac{300+n}{10}\big)(10)(16)$

Simplifying:

$10(600+n)=(300+n)16\\ 6000+10n=4800+16n$

And finally, we solve for $n$ :

$6000-4800=16n-10n\\ 1200=6n\\ 200=n$

So, the confectioner needs 200 lbs of chocolate that's 1 part cocoa butter and 15 parts caramel.

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