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Lina20 [59]
3 years ago
12

PLEASE DON'T SKIP Solve the system of equations.

Mathematics
1 answer:
Tems11 [23]3 years ago
7 0

                <u>2x + 3y = 1</u>

                <u>y = 3x + 15</u>

There's not much you can do with the first equation, because it has
two variables in it ... 'x'  and  'y' .  No matter how much you move them
around, you'll never be able to get either one equal to just a number. 
Is there any way you could get rid of one of the variables in the first
equation, and have just 1 letter in it to solve for ?

Absolutely !  The second equation tells you something that 'y' is <u>equal</u> to,
(3x + 15).  "EQUAL" is very powerful.  It means that wherever you see 'y',
you can put (3x + 15) in its place, and you won't change anything or
upset anything.  One thing you can do is take that (3x + 15) from the <span>
2nd</span> equation, and put it right into the first equation in place of 'y'. 
You'll see how that helps as soon as you do it.

             First equation:    <u>2x + 3y = 1</u>

         Substitute for 'y' :    2x + 3(<em>3x + 15</em>) = 1

 Remove parentheses:    2x + 3(3x) + 3(15) = 1
                                        2x +  9x    +    45  =  1

Combine the terms with 'x' in them:    11x + 45 = 1

Look what you have now !  An equation with only one variable in it !

Subtract  45  from each side:    11x = -44

Divide each side by  11 :          <em>  x = -4</em>

You're more than halfway there.  Now you know what 'x' is,
and you can use it with either equation to find what 'y' is.

-- If you use it with the first equation:     <u> 2x + 3y = 1</u>

       Put in the value of 'x':    2(<em>-4</em>) + 3y = 1

Remove the parentheses:      -8 + 3y = 1

        Add  8  to each side:              3y = 9

    Divide each side by  3 :              <em> y = 3</em>


-- If you use it with the 2nd equation:    <u>y = 3x + 15</u>
 
            Put in the value of  'x' :      y = 3(<em>-4</em>) + 15

       Remove the parentheses:      y = -12 + 15

Add numbers on the right side:   <em>  y = 3</em>  (same as the other way)

So there's your solution for the system of two equations:

        <em> x = -4</em>
<em>         y = 3</em>


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Anna35 [415]

Answer:

10m.

Step-by-step explanation:

Since there is no remainder we simply need to find the least common multiple of each of the lengths of Janice and Jasmin's strings until we find a multiple that matches for each. Like so...

2*1 = 2                    5*1 = 5

2*2 = 4                   5*2 = 10

2*3 = 6

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Finally, we have found the first common multiple which is 10m. That means that the shortest equal length for both Janice's and Jasmin's ribbon is 10m.

8 0
3 years ago
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3 0
3 years ago
Read 2 more answers
Michael bought four tacos and a burrito and paid $9.50. Noah bought two tacos and three burritos and paid $11. Based on the info
Afina-wow [57]
In order to solve this equation you could use guess and check with multiple choice, or you can set up a system of equations.
First we must define our variables:
x=price of taco
y=price of burrito
Michael bought 4 tacos (4x) and (+) and Burrito (y) for $9.50 (=9.5)
4x+y=9.50
Noah bought two tacos (2x) and (+) three burritos (3y) for (=) $11 (11)
2x+3y=11
To solve this system of equations you can easily see substitution as the easiest method. For substitution we must isolate one variable:
4x+y=9.50
y=-4x+9.5
We can now replace the y in the other equation:
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Then solve this equation to get the price of a taco (x)
2x-12x+28.5=11
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The price of a taco would be $1.75
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4 years ago
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Answer:

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3 0
3 years ago
What is the volume of the cube?
Jobisdone [24]
27 cubic inches
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