Advertisements
Advertisements
Question
Solve the following systems of equations:
3x − 7y + 10 = 0
y − 2x − 3 = 0
Solution
The given system of equation is
3x − 7y + 10 = 0 ...(i)
y - 2x - 3 = 0 ...(ii)
∴ y = 2x + 3 ...(iii)
Substituting y = 2x + 3 in (i), we get,
3x − 7y + 10 = 0
3x - 7(2x + 3) + 10 = 0
3x - 14x - 21 + 10 = 0
-11x - 11 = 0
-11x = 11
x = `11/-11` = - 1
Putting x = 1 in y = 2x + 3 equation (iii), we get,
y = 2x + 3
y = 2(- 1) + 3
y = - 2 + 3
y = 1
Hence, the solution of the given system of equations is x = - 1, y = 1.
APPEARS IN
RELATED QUESTIONS
Form the pair of linear equations for the following problems and find their solution by substitution method.
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹ 105 and for a journey of 15 km, the charge paid is ₹ 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
Solve the following simultaneous equations
`1/(3x)-1/(4y)+1=0`;
`1/(5x)+1/(2y)=4/15`
Solve the following systems of equations:
`x/2 + y = 0.8`
`7/(x + y/2) = 10`
Solve the following systems of equations:
`"xy"/(x + y) = 6/5`
`"xy"/(y- x) = 6`
Solve the following systems of equations:
x + y = 5xy
3x + 2y = 13xy
Solve the following set of simultaneous equation.
2x - 7y = 7; 3x + y = 22
Find the solution of the pair of the equation :
`3/x + 8/y = - 1; 1/x - 2/y = 2`, x, y ≠ 0
A person starts a job with a fixed salary and yearly increment. After 4 years his salary is ₹ 15000 and after 10 years it becomes ₹ 18000. Then find his monthly salary and increment
A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train was slower by 6 km/h it would have taken 6 hours more than the scheduled time. Find the length of the journey.
The sum of two numbers is 34. If 3 is subtracted from one number and 2 is added to another, the product of these two numbers becomes 260. Find the numbers.
