Advertisements
Advertisements
Question
Solve each of the following systems of equations by the method of cross-multiplication
3x + 2y + 25 = 0
2x + y + 10 = 0
Solution
The given system of equation is
3x + 2y + 25 = 0
2x + y + 10 = 0
Here
`a_1 = 3, b_1 = 2, c_1 = 25`
`a_2 = 2, b_2 = 1, c_2 = 10`
By cross-multiplication, we have
`=> x/(2xx 10-25xx 1) = (-y)/(3xx 10- 25xx 2) = 1/(3xx1 - 2xx2)`
`=> x/(20-25) = (-y)/(30-50) =- 1/(3-4)`
`=> x/(-5) = (-y)/(-20) = 1/(-1)`
Now `x/(-5) = 1/(-1)`
`=> x = (-5)/(-1) = 5`
And
`(-y)/(-20) = 1/(-1)`
`=> y/20 = 1`
=> y = -20
Hence, x = 5, y = 20 is the solution of the given system of equations.
APPEARS IN
RELATED QUESTIONS
Solve the following system of equations by cross-multiplications method.
`a(x + y) + b (x – y) = a^2 – ab + b^2`
`a(x + y) – b (x – y) = a^2 + ab + b^2`
For which values of a and b does the following pair of linear equations have an infinite number of solutions?
2x + 3y = 7
(a – b) x + (a + b) y = 3a + b – 2
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method
Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?
Solve the following systems of equations:
`x + 2y = 3/2`
`2x + y = 3/2`
Solve each of the following systems of equations by the method of cross-multiplication
`x/a = y/b`
`ax + by = a^2 + b^2`
Solve each of the following systems of equations by the method of cross-multiplication
5ax + 6by = 28
3ax + 4by = 18
Solve the system of equations by using the method of cross multiplication:
3x - 2y + 3 = 0,
4x + 3y – 47 = 0
Solve the system of equations by using the method of cross multiplication:
2x + y – 35 = 0,
3x + 4y – 65 = 0
The number of solutions of 3x + y = 243 and 243x - y = 3 is ______.
A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.
