Advertisements
Advertisements
प्रश्न
Solve the following pair of linear (Simultaneous ) equation using method of elimination by substitution :
2( x - 3 ) + 3( y - 5 ) = 0
5( x - 1 ) + 4( y - 4 ) = 0
Advertisements
उत्तर
Given equations are
2( x - 3 ) + 3( y - 5 ) = 0 ...(1)
5( x - 1 ) + 4( y - 4 ) = 0 ...(2)
From (1), we get
2x - 6 + 3y - 15 = 0
⇒ 2x + 3y = 21
⇒ 2x = 21 - 3y
⇒ x = `[ 21 - 3y ]/2`
From (2), we get
5( x - 1 ) + 4( y - 4 ) = 0
⇒ 5x - 5 + 4y - 16 = 0
⇒ 5x + 4y = 21 ....(3)
Substituting x = `[ 21 - 3y ]/2` in (3), we get
`5(( 21 - 3y )/2) + 4y = 21`
⇒ `[105 - 15y]/2 + 4y = 21`
⇒ `(105 - 15y + 8y)/2 =21`
105 - 7y = 42 - 105
⇒ -7y = -63
⇒ y = 9
Substituting y = 9 in
x = `[21 - 3y]/2`, we get
= `[ 21 - 3(9) ]/2`
`x= [ 21 - 27 ]/2`
`x = -6/2`
`x= -3`
∴ The solution is x = -3 and y = 9.
APPEARS IN
संबंधित प्रश्न
Solve the pair of linear (simultaneous) equation by the method of elimination by substitution :
2x - 3y = 7
5x + y= 9
Solve the pair of linear (simultaneous) equation by the method of elimination by substitution:
6x = 7y + 7
7y - x = 8
Solve the pair of linear (simultaneous) equation by the method of elimination by substitution :
y = 4x - 7
16x - 5y = 25
Solve the following pair of linear (simultaneous) equation using method of elimination by substitution:
3x + 2y =11
2x - 3y + 10 = 0
Solve the following pair of linear (simultaneous) equation using method of elimination by substitution :
2x - 3y + 6 = 0
2x + 3y - 18 = 0
Solve the following pairs of linear (simultaneous) equation using method of elimination by substitution:
`x/6 + y/15 = 4`
`x/3 - y/12 = 4 3/4`
Solve the following simultaneous equations by the substitution method:
2x + y = 8
3y = 3 + 4x
Solve the following simultaneous equations by the substitution method:
x + 3y= 5
7x - 8y = 6
Solve the following simultaneous equations by the substitution method:
2x + 3y = 31
5x - 4 = 3y
Solve the following simultaneous equations by the substitution method:
7x - 3y = 31
9x - 5y = 41
Solve the following simultaneous equations by the substitution method:
13 + 2y = 9x
3y = 7x
Solve the following pairs of equations:
`(6)/(x + y) = (7)/(x - y) + 3`
`(1)/(2(x + y)) = (1)/(3( x - y)`
Where x + y ≠ 0 and x - y ≠ 0
If a number is thrice the other and their sum is 68, find the numbers.
The sum of four times the first number and three times the second number is 15. The difference of three times the first number and twice the second number is 7. Find the numbers.
The age of the father is seven times the age of the son. Ten years later, the age of the father will be thrice the age of the son. Find their present ages.
In a ABC, ∠A = x°, ∠B = (2x - 30)°, ∠C = y° and also, ∠A + ∠B = one right angle. Find the angles. Also, state the type of this triangle.
Solve by the method of elimination
13x + 11y = 70, 11x + 13y = 74
