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Answer:
m∠ABC = m∠BED; Corresponding Angles Theorem
Step-by-step explanation:
<u>Given:</u> line BC is parallel to line ED m∠ABC = 70° m∠CED = 30°
<u>Prove:</u> m∠BEC = 40°
Statement Justification
1. line BC is parallel to line ED - Given
2. m∠ABC = 70° - Given
3. m∠CED = 30° - Given
4. m∠BEC + m∠CED = m∠BED - Angle Addition Postulate
5. m∠ABC = m∠BED - Corresponding Angles Theorem
6. m∠BEC + 30° = 70° - Substitution Property of Equality
7. m∠BEC = 40° Subtraction Property of Equality
Answer:
We have the system of equations:
y=1/3x+5
y=2/3x+5
To solve it graphically, we need to graph both lines and see in which point the lines intersect.
You can see the graph below, and you can see that the lines intersect in the point (0, 5)
Now, we can also solve this analytically.
We can use the fact that for the solution, we need y = y.
Then we can write:
(1/3)*x + 5 = (2/3)*x + 5
First, we can subtract 5 in both equations to get:
(1/3)*x = (2/3)*x
This only has a solution when x = 0.
Replacing x = 0 in one of the equations, we get:
y = (1/3)*0 + 5 = 5
Then the solution is x = 0, and y = 5, as we already could see in the graph.
