Advertisements
Advertisements
प्रश्न
Solve the following simultaneous equations by the substitution method:
0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5
उत्तर
The given equations are
0.5x + 0.7y = 0.74 ....(i)
0.3x + 0.5y = 0.5 ....(ii)
Now, consider equation
0.5x + 0.7y = 0.74
⇒ 0.5x = 0.74 - 0.7y
⇒ x = `(0.74 - 0.7y)/(0.5)` ....(iii)
Substituting the value of x in eqn. (ii), we get
`0.3((0.74 - 0.7y)/(0.5)) + 0.5y` = 0.5
⇒ `(0.222 - 0.21)/(0.5) + 0.5y` = 0.5
⇒ `(0.222 - 0.2y + 0.25)/(0.5)` = 0.5
⇒ 0.222 + 0.04y = 0.25
⇒ 0.04y = 0.028
⇒ y = `(0.028)/(0.04)`
= `(28)/(40)`
= `(7)/(10)`
= 0.7
Putting the value of y in eqn. (iii), we get
x = `(0.74 - 0.7(0.7))/(0.5)`
= `(0.74 - 0.49)/(0.5)`
= `(0.25)/(0.5)`
= `(25)/(50)`
= `(1)/(2)`
= 0.5
Thus, the solution set is (0.5, 0.7).
APPEARS IN
संबंधित प्रश्न
Solve the pair of linear (simultaneous) equation by the method of elimination by substitution :
8x + 5y = 9
3x + 2y = 4
Solve the pair of linear (simultaneous) equation by the method of elimination by substitution:
6x = 7y + 7
7y - x = 8
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 + 2y =11
2x - 3y + 10 = 0
Solve th following pair of linear (Simultaneous ) equation using method of elimination by substitution :
`[ 2x + 1]/7 + [5y - 3]/3 = 12`
`[3x + 2 ]/2 - [4y + 3]/9 = 13`
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:
7(y + 3) - 2(x + 2) = 14
4(y - 2) + 3(x - 3) = 2
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.
A two-digit number is such that the ten's digit exceeds thrice the unit's digit by 3 and the number obtained by interchanging the digits is 2 more than twice the sum of the digits. Find the number.
The ratio of passed and failed students in an examination was 3 : 1. Had 30 less appeared and 10 less failed, the ratio of passes to failures would have been 13 : 4. Find the number of students who appeared for the examination.
Solve by the method of elimination
x – y = 5, 3x + 2y = 25
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
