Advertisements
Advertisements
प्रश्न
Solve the following systems of equations:
`x + y/2 = 4`
`x/3 + 2y = 5`
उत्तर
The given system of equation is
`x + y/2 = 4` .......(i)
`x/3 + 2y = 5` ....(ii)
From (i), we get
`(2x + y)/2 = 4`
2x + y = 8
y = 8 - 2x
From (ii), we get
x + 6y = 15 ....(iii)
Substituting y = 8 - 2x in (iii), we get
x + 6(8 - 2x) = 15
`=> x + 48 - 12x = 15`
=> -11x = 15 - 48
=> -11x = -33
`=> x = (-33)/(-11) = 3`
Putting x = 3 in y = 8 - 2x we get
y = 8 - 2 x 3
= 8 - 6
= 2
y = 2
Hence, solution of the given system of equation is x= 3, y = 2
APPEARS IN
संबंधित प्रश्न
Solve the following system of equations by cross-multiplication method x + y = a – b; ax – by = a2 + b2
Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method
2x + y = 5
3x + 2y = 8
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
A fraction becomes `1/3` when 1 is subtracted from the numerator and it becomes `1/4` when 8 is added to its denominator. Find the fraction.
Solve the following systems of equations:
`sqrt2x + sqrt3y = 0`
`sqrt3x - sqrt8y = 0`
Solve the following systems of equations:
`4/x + 3y = 14`
`3/x - 4y = 23`
Solve each of the following systems of equations by the method of cross-multiplication :
x + 2y + 1 = 0
2x − 3y − 12 = 0
Solve each of the following systems of equations by the method of cross-multiplication :
2x + y = 35
3x + 4y = 65
Solve each of the following systems of equations by the method of cross-multiplication
x + ay = b
ax − by = c
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
bx + cy = a + b
`ax (1/(a - b) - 1/(a + b)) + cy(1/(b -a) - 1/(b + a)) = (2a)/(a + b)`
