-4x + 6y = 12
x + 2y = -10
First solve for x in the second equation
x + 2y = -10
x = -10 - 2y
Now we have a value for x so we can substitute it into the other equation
-4 (-10 - 2y) + 6y = 12
Now solve for y
40 + 8y + 6y = 12
40 + 14y = 12
14y = -28
y = -2
Now we have a value for y that we can plug into one of the original equations so we can solve for x
x + 2y = -10
x + 2(-2) = -10
x - 4 = -10
x = -6
Your solution set is
(-6, -2)
Angles ACD and ACE are supplementary. They combine to form a straight angle which is 180 degrees. Let x be the measure of angle ACE.
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(angle ACD) + (angle ACE) = 180
100 + x = 180
x = 180-100 .... subtract 100 from both sides
x = 80
<h3>angle ACE is 80 degrees</h3>
Focus on the top line angles for now.
Those two angles combine to the straight angle ABC, which is 180 degrees.
(angleABY) + (angleYBC) = angle ABC
(x+25)+(2x+50) = 180
(x+2x) + (25+50) = 180
3x+75 = 180
3x = 180-75
3x = 105
x = 105/3
x = 35
We'll use this x value to find that:
- angle YBC = 2x+50 = 2*35+50 = 70+50 = 120 degrees
- angle BEF = 5x-55 = 5*35-55 = 175-55 = 120 degrees
Angles YBC and BEF are corresponding angles (they are both in the northeast corner of their respective four-corner angle configuration). They are both 120 degrees. Since we have congruent corresponding angles, we have effectively proven that AC is parallel to DF. Refer to the converse of the corresponding angles theorem.
The regular version of the "corresponding angles theorem" says that if two lines are parallel, then the corresponding angles are congruent. The converse reverses the logic of the conditional statement. Meaning that if the corresponding angles are congruent, then the lines are parallel.
Answer:
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