Advertisements
Advertisements
Question
Solve the following simultaneous equations by the substitution method:
0.4x + 0.3y = 1.7
0.7x - 0.2y = 0.8
Advertisements
Solution
The given equations are
0.4x + 0.3y = 1.7 ....(i)
0.7x - 0.2y = 0.8 ....(ii)
Multiplying both the equations by 10, we get
4x + 3y = 17 ....(iii)
7x - 2y = 8 ....(iv)
Now, consider equation
4x + 3y = 17
⇒ 4x = 17 - 3y
⇒ x = `(17 - 3y)/(4)` ....(v)
Substituting the value of x in eqn. (iv), we get
`7((17 - 3y)/(4)) - 2y` = 8
⇒ `(119 - 21y)/(4) - 2y` = 8
⇒ `(119 - 21y - 8y)/(4)` = 8
⇒ 119 - 29y = 32
⇒ -29y = 32 - 119
⇒ -29y = -87
⇒ y = `(-87)/(-29)`
= 3
Putting the value of y in eqn. (v), we get
x = `(17 - 3(3))/(4)`
= `(17 - 9)/(4)`
= `(8)/(4)`
= 2
Thus, the solution set is (2, 3).
APPEARS IN
RELATED QUESTIONS
Solve the pair of linear (simultaneous) equations by the method of elimination by substitution:
8x + 5y = 9
3x + 2y = 4
Solve the following pair of linear (simultaneous) equation by the method of elimination by substitution:
0.2x + 0.1y = 25
2(x - 2) - 1.6y = 116
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 :
2x - 3y + 6 = 0
2x + 3y - 18 = 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 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:
3 - (x + 5) = y + 2
2(x + y) = 10 + 2y
Solve the following simultaneous equations by the substitution method:
7(y + 3) - 2(x + 2) = 14
4(y - 2) + 3(x - 3) = 2
The difference of two numbers is 3, and the sum of three times the larger one and twice the smaller one is 19. Find the two numbers.
If a number is thrice the other and their sum is 68, find the numbers.
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.
Solve by the method of elimination
2x – y = 3, 3x + y = 7
Solve by the method of elimination
x – y = 5, 3x + 2y = 25
Solve by the method of elimination
13x + 11y = 70, 11x + 13y = 74
