Advertisements
Advertisements
Question
Solve the following simultaneous equations by the substitution method:
2x + y = 8
3y = 3 + 4x
Advertisements
Solution
The given equations are
2x + y = 8 ....(i)
3y = 3 + 4x ....(ii)
Now, consider equation 2x + y = 8
⇒ y = 8 - 2x ....(iii)
Substituting the value of y in eqn. (ii), we get
3(8 - 2x) = 3 + 4x
⇒ 24 - 6x = 3 + 4x
⇒ 6x - 4x = 3 - 24
⇒ -10x = -21
⇒ x = `(21)/(10)`
Puutting the value of x in eqn. (iii), we get
y = `8 - 2(21/10)`
= `8 - (21)/(5)`
= `(40 - 21)/(5)`
= `(19)/(5)`
Thus, the solution set is `(21/10 , 19/5)`.
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 pair of linear (simultaneous) equation 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 :
y = 4x - 7
16x - 5y = 25
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 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 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:
5x + 4y - 23 = 0
x + 9 = 6y
Solve the following simultaneous equations by the substitution method:
0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5
Solve the following simultaneous equations by the substitution method:
0.4x + 0.3y = 1.7
0.7x - 0.2y = 0.8
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
A father's age is three times the age of his child. After 12 years, twice the age of father will be 36 more than thrice the age of his child. Find his present age.
* Question modified
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.
Samidha and Shreya have pocket money Rs.x and Rs.y respectively at the beginning of a week. They both spend money throughout the week. At the end of the week, Samidha spends Rs.500 and is left with as much money as Shreya had in the beginning of the week. Shreya spends Rs.500 and is left with `(3)/(5)` of what Samidha had in the beginning of the week. Find their pocket money.
Solve by the method of elimination
3(2x + y) = 7xy, 3(x + 3y) = 11xy
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
