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
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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.