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storchak [24]
3 years ago
14

1. Explain in a complete sentence if the point (2, -4) is the solution to the system of equations. x + y = -2 2x – y = 8

Mathematics
1 answer:
Temka [501]3 years ago
7 0
So, it says x + y = -2
we just plug in the numbers so,
2 + - 4 = -2
This equation is true and can also be written as
2 - 4 = -2

It also then says that 2x - y = 8
Again, you just plug in the numbers
2 * 2 - (-4) = 8 
This equation is true and can also be writen as,
2*2 + 4 = 8
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PLEASE ANSWER: 3 1/2 + (-7) x (2 2/3 + 1 1/2) = ?
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-\frac{77}{3}

Step-by-step explanation:

So we have the equation: 3\frac{1}{2} + (-7) * (2\frac{2}{3} + 1\frac{1}{2}). and I'm assuming you meant to do mixed fractions and not actually multiplying. 2 * 2/3. So the first thing to do is follow PEMDAS which essentially says Parenthesis first, Exponents next, Multiplication or Division, and then Addition or Subtract. So let's start by evaluating the 2 2/3 and 1 1/2. The first step is to combine 2 into the 2/3 and the 1 into 1/2. This is done by multiplying the 2 by the denominator of 3, and adding it to the numerator so: 2\frac{2}{3} = > \frac{(2*3)+2}{3} = > \frac{8}{3}. And you do this for the 1/2 as well: 1\frac{1}{2} = > \frac{(2*1)+1}{2}= > \frac{3}{2}.

Now when adding fractions, you can only add them when they have the same denominator, so we have the get 3/2 and 8/3 to have the same denominator. You can list the multiplies of 2 and 3 to try to find a LCM, but in this case, I'll just multiply 2 and 3, since they're really small numbers, also because 6 is the LCM. \frac{8}{3} * \frac{2}{2} = \frac{16}{6}. And now do this to the 3/2 you get: \frac{3}{2} * \frac{3}{3} = \frac{9}{6}. Now the inside of the parenthesis is: \frac{9}{6} + \frac{16}{6} = \frac{25}{6}. So now we have the equation: 3\frac{1}{2} -7 * \frac{25}{6} . Also notice how I got ride of the plus sign and made it negative? Think of it as having a 1 in front and simply distributing that to the -7, 1*(-7) becomes -7.

Now to multiply the fraction by a whole number you simply multiply the denominator and numerator, and you can think of the denominator of a whole number as a 1. So this gives you: \frac{-7}{1} * \frac{25}{6} = \frac{-7 * 25}{1 * 6} = -\frac{175}{6}. Now we have the equation: 3\frac{1}{2} - \frac{175}{6}. And to subtract these two numbers I'll make the 3 1/2 a fraction by multiplying the 3 by the denominator and adding it to the 1 which should become 7/2. And after that multiply both sides by 3/3 to get 21/6 so they have the same denominator. This gives you the equation: \frac{21}{6} - \frac{175}{6} = \frac{21-175}{6} = -\frac{154}{6}. Which can simplify by dividing both sides by 2 to get: -\frac{77}{3}

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2 years ago
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