X + 5y = 1 . . . . (1)
8x - 2y = 3 . . . .(2)
Solution 1.
From (1), x = 1 - 5y
substituting for x in (2), we have:
8(1 - 5y) - 2y = 3
8 - 40y - 2y = 3
8 - 42y = 3
42y = 5
y = 5/42
x = 1 - 5(5/42) = 1 - 25/42 = 17/42.
Solution 2.
Multiply (1) by 8, to get:
8x + 40y = 8 . . . . . (3)
(3) - (2) = 40y - (-2y) = 8 - 3
42y = 5
y = 5/42
substitute for y into (3), to get:
8x + 40(5/42) = 8
8x + 100/21 = 8
8x = 8 - 100/21 = 68/21
x = (68/21)/8 = 17/42
Answer:
x= 60°, y = 80°, z = 40°
Step-by-step explanation:
Look at the line substending 40° and Z°; you would see that both lines are parallel and so their angles are they the same.
Hence z= 40° { corresponding angles of parallel lines}
Similarly;
Look at the line substending 60° and x°; you would see that both lines are parallel and so their angles are they the same.
60° = x° { corresponding angles of parallel lines}
Now looking at the angle between x and y; let's call the angle between them r
And you would observe closely that r = z° = 40°{ vertically opposite angles are equal}
Note that x + r + y = 180°{ angle on a straight line}
y = 180° - ( x + r)
y = 180 - (60+40)
y = 180° - 100°
= 80°
The answer of t he trapezoid area problem is 112.
<span>Here's the rule. I'm SURE you learned it in Middle School. Or,
I guess I should say: I'm SURE it was taught in Middle School.
Vertical angles are equal.
"Vertical angles" are the pair of angles that don't share a side,
formed by two intersecting lines.
AND ... even if you forgot it since hearing it in Middle School,
it was clearly explained in the answer to the question that
you posted 9 minutes before this one.
In #8, 'x' and 'z' are vertical angles.
'y' and 116° are vertical angles.
In #9, 'B' and 131° are vertical angles.
In #10, 'B' and 135° are vertical angles.
For all of these, it'll also help you to remember that all the angles
on one side of any straight line add up to 180°. </span>