Advertisements
Advertisements
प्रश्न
Solve the following simultaneous equations by the substitution method:
7(y + 3) - 2(x + 2) = 14
4(y - 2) + 3(x - 3) = 2
Advertisements
उत्तर
The given equations are
7(y + 3) - 2(x + 2) = 14 ....(i)
4(y - 2) + 3(x - 3) = 2 ....(ii)
Consider
7(y + 3) - 2(x + 2) = 14
⇒ 7y + 21 - 2x - 4 = 14
⇒ -2x + 7y = -3
⇒ 2x - 7y = 3
⇒ 2x = 7y + 3
⇒ x = `(7y + 3)/(2)` ....(iii)
Now, consider equation
4(y - 2) + 3(x - 3) = 2
⇒ 4y - 8 + 3x - 9 = 2
⇒ 3x + 4y = 19
⇒ `3((7y + 3)/(2)) + 4y` = 19 ....[From (iii)]
⇒ `(21y + 9 + 8y)/(2)` = 19
⇒ 29y + 9 = 38
⇒ 29y = 29
⇒ y = 1
Substituting value of y in eqn. (iii), we get
x = `(7(1) + 3)/(2)`
= `(10)/(2)`
= 5
Thus, the solution set is (5, 1).
APPEARS IN
संबंधित प्रश्न
Solve the pair of linear (simultaneous) equations by the method of elimination by substitution:
8x + 5y = 9
3x + 2y = 4
Solve the pair of linear (simultaneous) equations by the method of elimination by substitution:
2x + 3y = 8,
2x = 2 + 3y
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:
2x + 7y = 39
3x + 5y = 31
Solve the following pair of linear (simultaneous) equation by the method of elimination by substitution:
1.5x + 0.1y = 6.2
3x - 0.4y = 11.2
Solve the following pair of linear (simultaneous) equation using method of elimination by substitution:
`[3x]/2 - [5y]/3 + 2 = 0`
`x/3 + y/2 = 2 1/6`
Solve the following simultaneous equations by the substitution method:
x + 3y= 5
7x - 8y = 6
Solve the following simultaneous equations by the substitution method:
5x + 4y - 23 = 0
x + 9 = 6y
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:
0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5
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.
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
2x – y = 3, 3x + y = 7
Solve by the method of elimination
`4/x + 5y` = 7, `3/x + 4y` = 5
The monthly income of A and B are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves ₹ 5,000 per month, find the monthly income of each
