Advertisements
Advertisements
Question
Solve the following simultaneous equations:
13a - 11b = 70
11a - 13b = 74
Advertisements
Solution
The given equation are
13a - 11b = 70 ....(i)
11a - 13b = 74 ....(ii)
Multiplying eqn. (i) by 13 and eqn. (ii) by 11, we get
169a - 143b = 910 ....(iii)
121a - 143b = 814 ....(iv)
Subtracting eqn. (iv) from eq. (iii), we get
48a = 96
⇒ a = 2
Subtracting the value of a in eqn. (i), we get
13(2) - 11b = 70
⇒ 26 - 11b = 70
⇒ -11b = 70 - 26
⇒ -11b = 44
⇒ b = -4
Thus, the solution set is (2, - 4).
APPEARS IN
RELATED QUESTIONS
For solving pair of equation, in this exercise use the method of elimination by equating coefficients:
y = 2x - 6; y = 0
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
41x + 53y = 135
53x + 41y = 147
Solve for x and y:
4x = 17 - `[ x - y ]/8`
2y + x = 2 + `[ 5y + 2 ]/3`
Solve :
11(x - 5) + 10(y - 2) + 54 = 0
7(2x - 1) + 9(3y - 1) = 25
Solve the following simultaneous equations :
2(3u - v) = 5uv
2(u + 3v) = 5uv
Solve the following pairs of equations:
`(x + y)/(xy)` = 2
`(x - y)/(xy)` = 6
Seven more than a 2-digit number is equal to two less than the number obtained by reversing the digits. The sum of the digits is 5. Find the number.
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes `(1)/(2)`. Find the fraction.
A person goes 8 km downstream in 40 minutes and returns in 1 hour. Determine the speed of the person in still water and the speed of the stream.
A solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol. How much of each solution should be used?
