Which of the following lines passes through the point of intersection of 7x+13y=20 and 17x-11y=6
Answers
Answer:
All equations that are satisfied with x = 1 and y = 1 passes through the point of intersection of 7x + 13y = 20 and 17x - 11y = 6.
Step-by-step explanation:
Given equations are:
7x + 13y = 20 --(i)
17x - 11y = 6 --(ii)
Solve the equations simultaneously,
On multiplying equation (i) by 11 and equation (ii) by 13, we get
=> 77x + 143y = 220
221x - 143y = 78
On adding,
=> 298x = 298
=> x = 1
Substituting x = 1 in equation ( i )
=> 7*1 + 13y = 20
=> 7 + 13y = 20
=> 13y = 20 - 7
=> 13y = 13
=> y = 1
Therefore the intersecting point is (1, 1)
Hence, all the equations that are satisfied on putting x = 1 and y = 1, passes through the point of intersection of 7x + 13y = 20 and 17x - 11y = 6.
To find
The equation of line passing though (1,1)
We know
The point slope form of a line is y - y₁ = m(x - x₁)
where m is the slope,
On substitution, we get
y - 1 = m(x - 1)
=> y - 1 = mx - m
=> y - mx = 1 - m
This is the equation of the line ,where m is the slope.