Advertisements
Advertisements
Question
Solve the following simultaneous equations by the substitution method:
x + 3y= 5
7x - 8y = 6
Advertisements
Solution
The given equations are
x + 3y= 5 ....(i)
7x - 8y = 6 ....(ii)
Now, consider equation
x + 3y = 5
⇒ x = 5 - 3y ....(iii)
Substituting the value of x in eqn. (ii), we get
7(5 - 3y) - 8y = 6
⇒ 35 - 21y - 8y = 6
⇒ 35 - 29y = 6
⇒ -29y = -29
⇒ y = 1
Putting the value of y in eqn. (ii), we get
x = 5 - 3(1)
= 5 - 3 = 2
Thus, the solution set is (2, 1).
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 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 :
2( x - 3 ) + 3( y - 5 ) = 0
5( x - 1 ) + 4( y - 4 ) = 0
Solve the following pair of linear (simultaneous) equation using method of elimination by substitution :
2x - 3y + 6 = 0
2x + 3y - 18 = 0
Solve the following simultaneous equations by the substitution method:
2x + y = 8
3y = 3 + 4x
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:
7x - 3y = 31
9x - 5y = 41
Solve the following simultaneous equations by the substitution method:
13 + 2y = 9x
3y = 7x
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
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 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
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.
Solve by the method of elimination
x – y = 5, 3x + 2y = 25
Solve by the method of elimination
`x/10 + y/5` = 14, `x/8 + y/6` = 15
Solve by the method of elimination
3(2x + y) = 7xy, 3(x + 3y) = 11xy
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
