Find the solution to the system of equations.
2 answers:
Answer:
x=1, y=3
Step-by-step explanation:
21x + 7y = 42
Divide this by 7
3x +y = 6
-5x +5y = 10
Divide this by 5
-x+y = 2
Subtract the two equations to eliminate y
3x +y = 6
-(-x+y = 2)
------------------------
3x +y = 6
+x-y = -2
------------------------
4x = 4
Divide by 4
x = 1
Now solve for y
-x+y = 2
-1 +y = 2
Add 1 to each side
y = 2+1
y =3
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Given:
Two lines intersect each other.
Consider the below figure attached with this question.
To find:
The value of x.
Solution:
If two lines intersect each other then the vertically opposite angles are congruent and their measures are equal.
In the given figure, the measures of two vertically opposite angles are (2x+29)° and (9x-13)°.
Divide both sides by -7.
Therefore, the value of x is 6.
Explanation:
There are numerous videos and web sites that can show you the process of copying an angle. Some are animated. The best we can do here is show you a diagram with instructions. Of course, your curriculum materials already provide that.
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1. Set the compass to a convenient radius. Use that to draw an arc through rays ED and EF, using point E as the center.
2. Without changing the compass setting, draw a similar arc using S as the center, making sure it crosses the line containing S and extends far enough to accommodate the following steps. (In the attached, we show a full circle, because the tool we used won't draw an arc with a specific radius.)
3. Mark the points where the arc crosses ED as G, and where it crosses EF as H. Mark the point where the arc crosses the line containing S as I.
4. Set the compass radius to the distance GH. Using I as the center draw an arc with that radius so that it crosses the one made in step 2. Call that intersection point J. (Again, we have shown a circle because of the limitations of the tool being used for our diagram.)
5. Draw ray SJ to complete the angle copy.
