geno3141

x = 2 - 3y

3x + 9y  =  6  --->  3(2 - 3y) + 9y  =  6

                                 6 - 9y + 9y  =  6

                                        6 - 0 = 6

                                              6  =  6   

There is no single answer; there are an infinite number of values that work.

If you rearranged the first equation to get  x + 3y  =  2  and then multiply this equation by 3, you would get     3x + 9y  =  6  which is exactly the same equation as the second equation. So any combination of numbers for x and y that solve the first equation also solves the second, and there are an infinite number of possible answers.     

x - 5y  =  7                                                 -->      x -   5y  =  7  

15y = 3x - 9    (subtract 3x from both sides)  -->  -3x + 15y  =  -9

To cancel out the y-term, get both coefficients to by 15 by multiplying the top equation by 3:

                   x -    5y  = 7         (times 3)      -->    3x  -  15y  =  21

           (leave the second equation alone)      -->   -3x + 15y  = -9 

                   (add down the comumns)          -->     0x + 0y  =  12

This problem is impossible to solve because all the x's and y's disappear.

The first equation is:  3x - 15y  =  21; the second equation (after you multiply it by -1) is:  3x - 15y  =  9;

there is no way that 3x - 15y can be both 21 and 9; therefore, impossible.

When you divide by a fraction, you multiply by the reciprocal.

√5 / (1/13)  =  √5 · (13/1)  =  √5 · 13  =  13√5

6x + 5y  =  3              (multiply this equation by 2)  -->     12x + 10y  =  6

9x - 10y  =  -48          (leave this equation alone)    -->       9x - 10y  =  -48

                                                                                       -------------------

                                      add down the columns:                21x         = -42     --->   x  =  -2

Substitute -2 back in for x in the first equation:

6(-2) + 5y  =  3                                       Since x = -2  and  y = 3, the solution is (-2, 3).

  -12 + 5y  =  3                                        Thus, a = -2  and  b = 3, and a + b = 1

           5y  =  15

             y  =  3

Let  L =  larger number    and   S = smaller number

L + S  =  17        The sum of the two numbers is 17.

L  =  2 + 2S        The larger number is two more than twice the smaller.

Substitute the value of L from the second equation into the first equation:

(2 + 2S) + S  =  17

2 + 3S  =  17

      3S  =  15

        S  =  5   

        L  =  12

√12  =  √4 · √3  =  2√3 

-1/3 x 21/1               Multiply the numerator times the numerator and the denominator times the denominator.

=  -21/3                    Now, simplify.   -21 ÷ 3  =  7

=  -7

You'll need to complete the problem.

Call the lenght L.  Since the length is 5 more than the width, the width is L - 5.

Perimeter = (L) + (L - 5) + (L) + (L - 5)  =  26

Simplifying:  4L - 10  =  26

                         4L  =  36

                           L  =  9                          W  =  L - 5  =  9 - 5  =  4

What are the choices?