Solve:(1/7)x +(1/6)y =3 ; (1/2)x - (1/3)y =5
1 answer:
Answer:
(14, 6 )
Step-by-step explanation:
Given
x +
y = 3 ( multiply through by 42 to clear the fractions )
6x + 7y = 126 → (1)
x -
y = 5 ( multiply through by 6 to clear the fractions )
3x - 2y = 30 → (2)
Multiplying (2) by - 2 and adding to (1) will eliminate the x- term
- 6x + 4y = - 60 → (3)
Add (1) and (3)term by term to eliminate x
11y = 66 ( divide both sides by 11 )
y = 6
Substitute y = 6 into either of the 2 equations and evaluate for x
Substituting into (1)
6x + 7(6) = 126
6x + 42 = 126 ( subtract 42 from both sides )
6x = 84 ( divide both sides by 6 )
x = 14
Solution is (14, 6 )
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Answer:
Segment BF = 16
Step-by-step explanation:
The given theorem states that a line parallel to one side of a triangle divides the other two sides proportionately
The given theorem is the Triangle Proportionality Theorem
According to the theorem, given that segment DE is parallel to segment BC, we have;
Therefore;
Which gives;
Similarly, given that EF is parallel to AB, we get;
Therefore;
Which gives;
Therefore, the statement that can be proved using the given theorem is segment BF = 16.