Find the point of intersection of the lines:

Find the point of intersection of the lines:
$\frac{x}{y+1}$ = $\frac{3}{5}$ and $\frac{x+1}{5}$ = $\frac{y}{2}$

Answers

Point of intersection of the lines.

$\frac{x}{y+1}$ = $\frac{3}{5}$

5x = 3y + 3

5x - 3y = 3 ......................(i)

and

$\frac{x+1}{5}$ = $\frac{y}{2}$

2x + 2 = 5y

2x - 5y = -2 ..................(ii)

Multiply eqn (i) by 2 and eqn(ii) by 5

10x - 6y = 6
10x - 25y = -10

19y = 16

y = $\frac{16}{19}$

Substitute y = $\frac{16}{19}$ in eqn (ii)

2x + 2 = 5($\frac{16}{19}$), 2x + 2 = $\frac{80}{19}$;

2x = $\frac{80-38}{19}$ = $\frac{42}{19}$

38x = 42,

x = $\frac{21}{19}$

The two lines intersect at

($\frac{21}{19},\frac{16}{19}$) or (21,16)

---

johnmulu answered the question on June 8, 2017 at 08:04

Next: What are the factors influencing deposition by ocean waves?
Previous: Two lines whose equations are 2x + 3y = 6 and 9y = 6x - 18 intersect at A. find the co-ordinates of A.

View More Mathematics Questions and Answers | Return to Questions Index

Exams With Marking Schemes

• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Grade 9
• PP1
• PP2
• Playgroup
• Form 1
• Form 2
• Form 3
• Form 4

Related Questions

• Find the point of intersection of these two straight lines:(Solved)
  

  Find the point of intersection of these two straight lines:
  2y + 3y + 1 = 0 and 2x - y = 2.

  Date posted: June 8, 2017.  Answers (1)

• Solve the simultaneous equations. (Solved)
  

  Solve the simultaneous equations.
  y = 2(x - 1) and y = 10 - x hence find the value of a if
  y² = 4ax

  Date posted: June 8, 2017.  Answers (1)

• Given that x = 2, find the values of y and z for the equations: (Solved)
  

  Given that x = 2, find the values of y and z for the equations:
  x + y - z = -1 and
  x - 2y + z = -7.

  Date posted: June 8, 2017.  Answers (1)

• When asked to find $\frac{7}{18}$ of a number, a girl made the mistake finding $\frac{7}{8}$ of it. Her answer was too big by 105. Find the number. (Solved)
  

  When asked to find $\frac{7}{18}$ of a number, a girl made the mistake finding $\frac{7}{8}$ of it. Her answer was too big by 105. Find the number.

  Date posted: June 8, 2017.  Answers (1)

• Four people Jane, Mary, Calley and David are business partners. They share profit made as follows: Mary gets twice as much as Calley..(Solved)
  

  Four people Jane, Mary, Calley and David are business partners. They share profit made as follows: Mary gets twice as much as Calley. Jane gets sh 1 200 more than Calley. During a given period they made a profit of sh 89 200. Determine the share of Calley.

  Date posted: June 8, 2017.  Answers (1)

• The sum of four consecutive even numbers is 108. Find the numbers. (Solved)
  

  The sum of four consecutive even numbers is 108. Find the numbers.

  Date posted: June 8, 2017.  Answers (1)

• Betty is 8 years older than Hilda and 3 years older than Matilda. If the sum of their age is 37 years, find the age of Matilda. (Solved)
  

  Betty is 8 years older than Hilda and 3 years older than Matilda. If the sum of their age is 37 years, find the age of Matilda.

  Date posted: June 8, 2017.  Answers (1)

• A farmer has twice as many goats as cows and half as many pigs as cows. If he has 45 pigs in his farm, how many animals does he keep altogether? (Solved)
  

  A farmer has twice as many goats as cows and half as many pigs as cows. If he has 45 pigs in his farm, how many animals does he keep altogether?

  Date posted: June 8, 2017.  Answers (1)

• Mary is 5 times as old as her daughter. 15 years from now, the daughter will be half as old as her mother. What is the present age of each. (Solved)
  

  Mary is 5 times as old as her daughter. 15 years from now, the daughter will be half as old as her mother. What is the present age of each.

  Date posted: June 8, 2017.  Answers (1)

• A man is now three times as old as the daughter. In 12 years times he will be twice as old as his daughter. Find their present ages. (Solved)
  

  A man is now three times as old as the daughter. In 12 years times he will be twice as old as his daughter. Find their present ages.

  Date posted: June 8, 2017.  Answers (1)

• Kamau, Weko and Suna are three casual workers in an organisation. Kamau earns twice as much as Weko and Suna earns sh 40 more than Kamau. If the total earnings are sh 1 090, Calculate the difference between Weko's and Suna's earnings. (Solved)
  

  Kamau, Weko and Suna are three casual workers in an organisation. Kamau earns twice as much as Weko and Suna earns sh 40 more than Kamau. If the total earnings are sh 1 090, Calculate the difference between Weko's and Suna's earnings.

  Date posted: June 8, 2017.  Answers (1)

• A fuel dealer makes a gain of sh 450 for every 1000 litres of petrol sold and sh 380 for every 1000(Solved)
  

  A fuel dealer makes a gain of sh 450 for every 1000 litres of petrol sold and sh 380 for every 1 000 litres diesel sold. In a certain month the dealer sold twice as much petrol as diesel. If the total fuel sold that month was 600 000 litres, find the dealers profit for the month.

  Date posted: June 8, 2017.  Answers (1)

• The greatest of the three consecutive odd numbers is (2n + 3). If their sum is 105, find the value of n. (Solved)
  

  The greatest of the three consecutive odd numbers is (2n + 3). If their sum is 105, find the value of n.

  Date posted: June 8, 2017.  Answers (1)

• Two thirds of a number added to one ninth of the number is 20 less than the number. Find the number. (Solved)
  

  Two thirds of a number added to one ninth of the number is 20 less than the number. Find the number.

  Date posted: June 8, 2017.  Answers (1)

• Two thirds of a number exceeds three fifths of the number by 40. Find the number. (Solved)
  

  Two thirds of a number exceeds three fifths of the number by 40. Find the number.

  Date posted: June 8, 2017.  Answers (1)

• Simplify $\frac{x\;-\;1}{x}$ - $\frac{2x\;+1\;}{3x}$ Hence solve $\frac{x\;-\;1}{x}$ - $\frac{2x\;+\;1}{3x}$ = $\frac{2}{3}$(Solved)
  

  Simplify $\frac{x\;-\;1}{x}$ - $\frac{2x\;+1\;}{3x}$ Hence solve $\frac{x\;-\;1}{x}$ - $\frac{2x\;+\;1}{3x}$ = $\frac{2}{3}$

  Date posted: June 7, 2017.  Answers (1)

• Find k if(Solved)
  

  Find k if
  $\frac{4x\;-\;1}{2}$ = $\frac{14x\;+\;k}{7}$

  Date posted: June 7, 2017.  Answers (1)

• Given that 6 - 3x = $\frac{1}{2}(x-2)$, find the value of x. (Solved)
  

  Given that 6 - 3x = $\frac{1}{2}(x-2)$, find the value of x.
  

  Date posted: June 7, 2017.  Answers (1)

• Solve the equation(Solved)
  

  Solve the equation
  $\frac{3x}{2}$ - $\frac{x\;-\;1}{3}$ = $\frac{1}{2}(3x\;-\;2)$

  Date posted: June 7, 2017.  Answers (1)

• Solve the equation (Solved)
  

  Solve the equation
  $\frac{1}{3}(x\;+\;4)$ - $\frac{1}{2}(2x$ - 4) = 2

  Date posted: June 7, 2017.  Answers (1)