Advertisements
Advertisements
प्रश्न
Solve the following simultaneous equations by the substitution method:
7x - 3y = 31
9x - 5y = 41
उत्तर
The given equations are
7x - 3y = 31 ...(i)
9x - 5y = 41 ....(ii)
Now, consider equation
7x - 3y = 31
⇒ 7x = 31 + 3y
⇒ x = `(31 + 3y)/(7)` ....(iii)
Substituting the value of x in eqn. (ii), we get
`9((31 + 3y)/(7)) - 5y` = 41
⇒ `(279 + 27y)/(7) - 5y` = 41
⇒ `(279 + 27y - 35y)/(7)` = 41
⇒ 279 - 8y = 287
⇒ -8y = 8
⇒ y = -1
Putting the value of y in eqn. (iii). we get
x = `(31 + 3(-1))/(7)`
= `(31 - 3)/(7)`
= `(28)/(7)`
= 4
Thus, the solution set is (4, -1).
APPEARS IN
संबंधित प्रश्न
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 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 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:
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.
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.
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
2x – y = 3, 3x + y = 7
Solve by the method of elimination
x – y = 5, 3x + 2y = 25
Five years ago, a man was seven times as old as his son, while five year hence, the man will be four times as old as his son. Find their present age
