Question

#12 and 13 please. Need help.

Answer 1

Problem 12:  Recognize that 4x+10 and 2y-30 are "vertical angles" and are thus equal to each other.  Thus, 4x+10=2y-30.  Similarly, 2(y+25) and 13x are vertical angles, so that 2(y+25) = 13x.

Here we have 2 equations in the 2 unknowns x and y.

Rewriting the first equation:  4x-2y=-20.  Rewriting the second:  13x-2y=50.

We must solve this system of linear equations simultaneously:

4x  -  2y  =  -20   or  -4x + 2y = 20
13x - 2y  = 50          13x - 2y  = 50
                                ---------------------
                                  9x          = 70
                                    x  = 70/9

Use either of the given equations to find the value of y, given that x = 70/9.

13x - 2y = 50

13(70)
----------  - 2y = 50   gives us  2y = 50 + 13(70)/9, or 2y = 50 + 101.11
      9                                                                                = 151.11
                                           So y = 75.5

Review:  Recognize vertical angles when you see them.  A pair of vertical angles are equal to one another.